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BEGIN:VEVENT
SUMMARY:Colva Roney-Dougal (The University of St Andrews)
DTSTART;VALUE=DATE-TIME:20201008T150000Z
DTEND;VALUE=DATE-TIME:20201008T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/1
DESCRIPTION:Title: F
inite simple groups and complexity class NP\nby Colva Roney-Dougal (Th
e University of St Andrews) as part of GOThIC - Ischia Online Group Theory
Conference\n\n\nAbstract\nThis talk will describe connections between str
uctural results about the finite simple groups and the complexity of compu
tational algorithms for permutation groups.\n\nThe first part of the talk
will discuss the base size of a permutation group\, an invariant which det
ermines the complexity of many permutation group algorithms. We will prese
nt a new\, optimal\, bound on the base size of the primitive groups that a
re not large base. After this\, we will discuss some group-theoretic quest
ions for which there is no known polynomial time solution. In particular\,
we shall present a new approach to computing the normaliser of a primitiv
e group $G$ in an arbitrary subgroup $H$ of $S_{n}$. Our method runs in qu
asipolynomial time $O(2^{log^3 n})$\, whereas the previous best known algo
rithm required time $O(2^n)$.\n\nThis is partly joint work with Mariapia M
oscatiello (Padova)\, and partly with Sergio Siccha (Siegen).\n
LOCATION:https://researchseminars.org/talk/GOThIC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Jaikin-Zapirain (Autonomous University of Madrid)
DTSTART;VALUE=DATE-TIME:20201015T150000Z
DTEND;VALUE=DATE-TIME:20201015T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/2
DESCRIPTION:Title: I
ntersection of subgroups in a surface group\nby Andrei Jaikin-Zapirain
(Autonomous University of Madrid) as part of GOThIC - Ischia Online Group
Theory Conference\n\n\nAbstract\nLet $G$ be a surface group\, i.e the fun
damental group of a compact surface. Denote by $d(G)$ the number of genera
tors of $G$ and by $\\chi(G)$ the Euler characteristic of $G$. We put $\\b
ar \\chi(G) = \\max\\{0\, −\\chi(G)\\}$.\n\nIn this talk I will explain
the following two results. In the first result we prove that for any two f
initely generated subgroups $U$ and $W$ of $G$\,\n\n$$\n\\sum_{x \\in U\\b
ackslash G / W} \\bar \\chi (U \\cap x W x^{-1}) \\le \\bar \\chi(U) \\cdo
t \\bar\\chi(W).\n$$\nFrom this we obtain the Strengthened Hanna Neumann c
onjecture for non-solvable surface groups. In the second result we show th
at if $R$ is a retract of $G$\, then for any finitely generated subgroup $
H$ of $G$\,\n$$\nd(R \\cap H) \\le d(H).\n$$\nThis implies the Dicks-Ventu
ra inertia conjecture for free groups. The talk is based on a joint work w
ith Yago Antolín.\n
LOCATION:https://researchseminars.org/talk/GOThIC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anitha Thillaisundaram (University of Lincoln)
DTSTART;VALUE=DATE-TIME:20201022T150000Z
DTEND;VALUE=DATE-TIME:20201022T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/3
DESCRIPTION:Title: T
he congruence subgroup property for multi-EGS groups\nby Anitha Thilla
isundaram (University of Lincoln) as part of GOThIC - Ischia Online Group
Theory Conference\n\n\nAbstract\nIt was proved by G. A. Fernández-Alcober
\, A. Garrido and J. Uria-Albizuri that the branch Grigorchuk-Gupta-Sidki
(GGS) groups possess the congruence subgroup property. This result was ext
ended to all branch multi-GGS groups by A. Garrido and J. Uria-Albizuri. T
he extended Gupta-Sidki (EGS) groups\, which were the first examples of fi
nitely generated branch groups without the congruence subgroup property\,
were constructed by Pervova. In this talk\, we consider a natural generali
sation of multi-GGS and EGS groups\, and demonstrate their unexpected beha
viour concerning the congruence subgroup property. This is joint work with
J. Uria-Albizuri.\n
LOCATION:https://researchseminars.org/talk/GOThIC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bettina Eick (Technical University of Braunschweig)
DTSTART;VALUE=DATE-TIME:20201029T160000Z
DTEND;VALUE=DATE-TIME:20201029T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/4
DESCRIPTION:Title: G
roups and their integral group rings\nby Bettina Eick (Technical Unive
rsity of Braunschweig) as part of GOThIC - Ischia Online Group Theory Conf
erence\n\n\nAbstract\nThe integral group ring $\\mathbb{Z} G$ of a group $
G$ plays an important role in the theory of integral representations. This
talk gives a brief introduction to this topic and then shows how such gro
up rings can be investigated using computational tools. In particular\, th
e quotients $I^n(G)/I^{n+1}(G)$\, where $I^n(G)$ is the $n$-th power ideal
of the augmentation ideal $I(G)$\, are an interesting invariant of the gr
oup ring $\\mathbb{Z} G$ and we show how to determine them for given $n$ a
nd given finitely presented $G$. We then exhibit a variety of example appl
ications for finite and infinite groups $G$.\n
LOCATION:https://researchseminars.org/talk/GOThIC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derek J. S. Robinson (University of Illinois at Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20201105T160000Z
DTEND;VALUE=DATE-TIME:20201105T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/5
DESCRIPTION:Title: T
he seriality problem for Sylow-permutable subgroups in locally finite grou
ps\nby Derek J. S. Robinson (University of Illinois at Urbana-Champaig
n) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract
\nA subgroup $H$ of a group $G$ is said to be weakly Sylow permutable in $
G$ if $HP=PH$ for all Sylow subgroups $P$ of $G$ and all primes $p$ dividi
ng orders of elements of $H$. Otto Kegel proved that if $G$ is finite\, th
en $H$ is subnormal in $G$. This does not hold for infinite groups. The Se
riality Problem is whether Kegel’s theorem can be extended to locally fi
nite groups if "subnormal” is replaced by “serial”. I will discuss t
he background to the problem and recent progress towards its solution.\n
LOCATION:https://researchseminars.org/talk/GOThIC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Bors ((Johann Radon Institute for Compu- tational and Ap
plied Mathematics)
DTSTART;VALUE=DATE-TIME:20201112T160000Z
DTEND;VALUE=DATE-TIME:20201112T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/6
DESCRIPTION:Title: G
roups with few automorphism orbits\nby Alexander Bors ((Johann Radon I
nstitute for Compu- tational and Applied Mathematics) as part of GOThIC -
Ischia Online Group Theory Conference\n\n\nAbstract\nLet $G$ be a group\,
and consider the natural action of the automorphism group of $G$ on $G$. T
he orbits of this action are called the automorphism orbits of $G$. In thi
s talk\, we will give an overview of known results concerning groups with
finitely many automorphism orbits\, including results where $G$ is assumed
to have a concrete\, small number of automorphism orbits\, such as $G$. W
e will then speak in more detail about a result\, achieved in collaboratio
n with Stephen Glasby from UWA (Perth)\, which provides a full classificat
ion of the finite $2$-groups with exactly three automorphism orbits.\n
LOCATION:https://researchseminars.org/talk/GOThIC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramón Esteban-Romero (Polytechnic University of Valencia)
DTSTART;VALUE=DATE-TIME:20201119T160000Z
DTEND;VALUE=DATE-TIME:20201119T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/7
DESCRIPTION:Title: T
riply factorised groups and skew left braces\nby Ramón Esteban-Romero
(Polytechnic University of Valencia) as part of GOThIC - Ischia Online Gr
oup Theory Conference\n\n\nAbstract\nThe Yang-Baxter equation is a consist
ency equation of the statistical mechanics\nproposed by Yang [Yang67] and
Baxter\n[Baxter73] that describes the interaction of many particles in som
e scattering\nsituations. This equation lays the foundation for the theory
of quantum\ngroups and Hopf algebras. During the last years\, the study s
uggested by\nDrinfeld [Drinfeld92] of the so-called\nset-theoretic solutio
ns of the Yang-Baxter equation has motivated the\nappearance of many algeb
raic structures. Among these structures we\nfind the *skew left braces*\,
introduced by Guarnieri and\nVendramin [GuarnieriVendramin17] as a general
isation of the\nstructure of left brace defined by Rump [Rump07]. It cons
ists of a set $B$\nwith two operations $+$ and $\\cdot$\, not necessarily
commutative\, that give $B$ two structures of\ngroup linked by a modified
distributive law.\n\nThe multiplicative group $C=(B\, {\\cdot})$ of a skew
left brace $(B\, {+}\, {\\cdot})$\nacts on the\nmultiplicative group $K=(
B\, {+})$ by means of an action $\\lambda\\colon\nC\\longrightarrow \\oper
atorname{Aut}(K)$ given by\n$\\lambda(a)(b)=-a+a\\cdot b$\, for $a$\, $b\\
in B$. With respect to this\naction\, the identity map $\\delta\\colon C\\
longrightarrow K$ becomes a\nderivation or $1$-cocycle with respect to $\\
lambda$. In the semidirect\nproduct $G=[K]C=\\{(k\,c)\\mid k\\in K\, c\\in
C\\}$\, there is a\ndiagonal-type subgroup $D=\\{(\\delta(c)\, c)\\mid c\
\in C\\}$ such that\n$G=KD=CD$\, $K\\cap D=C\\cap D=1$. This approach was
presented by\nSysak in [Sysak11-PortoCesareo] and motivates the use of\nte
chniques of group theory to study skew left braces.\n\nWe present in this
talk some applications of this approach to obtain\nsome results about skew
left braces. These results have been obtained\nin collaboration with Adol
fo Ballester-Bolinches.\n\nThis work has been supported by the research gr
ants\nPGC2018-095140-B-I00 from the Ministerio de Ciencia\,\n Innovaci\\'
on y Universidades (Spanish Government)\, the\nAgencia Estatal de Investig
aci\\'on (Spain)\, and FEDER (European\nUnion)\, and PROMETEO/2017/057 fro
m the Generalitat\n(Valencian Community\, Spain).\n\nReferences\n\n[Baxter
73] R. Baxter. Eight-vertex model in lattice statistics and one-dimensiona
l\nanisotropic Heisenberg chain. I. Some fundamental eigenvectors. Ann.\nP
hysics\, 76(1):1–24\, 1973.\n\n[Drinfeld92] V. G. Drinfeld. On some unso
lved problems in quantum group theory.\nIn P. P. Kulish\, editor\, Quantum
groups. Proceedings of workshops held\nin the Euler International Mathema
tical Institute\, Leningrad\, fall 1990\,\nvolume 1510 of Lecture Notes in
Mathematics\, pages 1–8. Springer-Verlag\,\nBerlin\, 1992.\n\n[Guarnier
iVendramin17] L. Guarnieri and L. Vendramin. Skew-braces and the Yang-Baxt
er equation. Math. Comp.\, 86(307):2519–2534\, 2017.\n\n[Rump07] W. Rump
. Braces\, radical rings\, and the quantum Yang-Baxter equation.\nJ. Algeb
ra\, 307:153–170\, 2007.\n\n[Sysak11-PortoCesareo] Y. P. Sysak. Products
of groups and quantum Yang-Baxter equation.\nNotes of a talk in Advances
in Group Theory and Applications\, Porto\nCesareo\, Lecce\, Italy\, 2011.\
n\n[Yang67] C. N. Yang. Some exact results for many-body problem in one di
mension\nwith repulsive delta-function interaction. Phys. Rev. Lett\, 19:1
312–1315\,\n1967\n
LOCATION:https://researchseminars.org/talk/GOThIC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urban Jezernik (Alfréd Rényi Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20201126T160000Z
DTEND;VALUE=DATE-TIME:20201126T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/8
DESCRIPTION:Title: D
iameters of groups\nby Urban Jezernik (Alfréd Rényi Institute of Mat
hematics) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nA
bstract\nThe diameter of a finite group $G$ equipped with a generating set
$S$ is the smallest number $k$ so that every element of $G$ can be writte
n as a product of at most $k$ elements from $S$. We will take a look at ho
w large or small these diameters can (conjecturally) be\, and what the gen
eric situation is like.\n
LOCATION:https://researchseminars.org/talk/GOThIC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Tracey (University of Oxford)
DTSTART;VALUE=DATE-TIME:20201203T160000Z
DTEND;VALUE=DATE-TIME:20201203T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/9
DESCRIPTION:Title: O
n the Fitting height and insoluble length of a finite group\nby Gareth
Tracey (University of Oxford) as part of GOThIC - Ischia Online Group The
ory Conference\n\n\nAbstract\nA classical result of Baer states that an el
ement x of a finite group $G$ is contained in the Fitting subgroup $F(G)$
of $G$ if and only if $x$ is a left Engel element of $G$. That is\, $x$ is
in $F(G)$ if and only if there exists a positive integer $k$ such that $[
g\, x\, ...\, x]$ (with $x$ appearing $k$ times\, and using the convention
$[x_1\, x_2\, x_3\, \\dots\, x_k] := [[\\dots [[x_1\, x_2]\, x_3]\, ...]\
, x_k])$ is trivial for all $g$ in $G$. The result was generalised by E. K
hukhro and P. Shumyatsky in a 2013 paper via an analysis of the sets $E(G(
k))= \\{[g\, x\, ...\, x]: g \\in G\\}$.\n\nIn this talk\, we will continu
e to study the properties of these sets\, concluding with the proof of two
conjectures made in said paper. As a by-product of our methods\, we also
prove a generalisation of a result of Flavell\, which itself generalises W
ielandt's Zipper Lemma and provides a characterisation of subgroups contai
ned in a unique maximal subgroup. We also derive a number of consequences
of our theorems\, including some applications to the set of odd order elem
ents of a nite group inverted by an involutory automorphism. Joint work wi
th R.M. Guralnick.\n
LOCATION:https://researchseminars.org/talk/GOThIC/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donald S. Passman (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20201210T160000Z
DTEND;VALUE=DATE-TIME:20201210T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/10
DESCRIPTION:Title:
Polynomial Identities\, Permutational Groups and Rewritable Groups\nby
Donald S. Passman (University of Wisconsin-Madison) as part of GOThIC - I
schia Online Group Theory Conference\n\n\nAbstract\nWe first study groups
whose group algebras satisfy a polynomial identity. We then consider permu
tational groups and rewritable groups. We discuss the known characterizati
ons of such groups and the relationships between these three group-theoret
ic properties and also between the proofs of their corresponding main theo
rems. Finally we discuss certain parameters associated with these conditio
ns and we mention a number of examples of interest.\n
LOCATION:https://researchseminars.org/talk/GOThIC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Matucci (Università di Milano-Bicocca)
DTSTART;VALUE=DATE-TIME:20201217T160000Z
DTEND;VALUE=DATE-TIME:20201217T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/11
DESCRIPTION:Title:
On Finitely Presented Groups that Contain $\\mathbb{Q}$\nby Francesco
Matucci (Università di Milano-Bicocca) as part of GOThIC - Ischia Online
Group Theory Conference\n\n\nAbstract\nIt is a consequence of Higman's emb
edding theorem that the additive group $\\mathbb{Q}$ of rational numbers c
an be embedded into a finitely presented group. Though Higman's proof is c
onstructive\, the resulting group presentation would be very large and unp
leasant. In 1999\, Martin Bridson and Pierre de la Harpe asked for an expl
icit and "natural" example of a finitely presented group that contains an
embedded copy of $\\mathbb{Q}$. In this talk\, we describe some solutions
to the Bridson - de la Harpe problem related to Richard Thompson's groups
F\, T\, and V. Moreover\, we prove that there exists a group containing $\
\mathbb{Q}$ which is simple and has type F infinity. This is joint work wi
th Jim Belk and James Hyde.\n
LOCATION:https://researchseminars.org/talk/GOThIC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Lubotzky (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20210114T150000Z
DTEND;VALUE=DATE-TIME:20210114T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/12
DESCRIPTION:Title:
Stability\, non-approximated groups and high-dimensional expanders\nby
Alex Lubotzky (Hebrew University of Jerusalem) as part of GOThIC - Ischia
Online Group Theory Conference\n\n\nAbstract\nSeveral well-known open que
stions\, such as: "are all groups sofic or hyperlinear?"\, have a common f
orm: can all groups be approximated \nby asymptotic homomorphisms into the
symmetric groups $\\mathrm{Sym}(n)$ (in the sofic case) or the unitary g
roups $U(n)$ (in the hyperlinear case)?\n\n In the case of $U(n)$\, t
he question can be asked with respect to different metrics and norms. \n
We answer\, for the first time\, some of these versions\, showing that
there exist finitely presented groups which are not approximated by $U(n
)$ with respect to the Frobenius ($=L_2$) norm and many other norms.\n\n
The strategy is via the notion of "stability": Some higher dimensional c
ohomology vanishing phenomena is proven to imply stability. Using Garland
method ( a.k.a. high dimensional expanders as quotients of Bruhat-Tits bu
ildings)\, it is shown that some non-residually-finite groups are stabl
e and hence cannot be approximated. These groups are central extensions o
f some lattices in p-adic Lie groups (constructed via a p-adic version of
a result of Deligne).\n\n All notions will be explained. Based
on joint works with M. De Chiffre\, L. Glebsky and A. Thom and with I. Op
penheim .\n
LOCATION:https://researchseminars.org/talk/GOThIC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Giannelli (Università di Firenze)
DTSTART;VALUE=DATE-TIME:20210204T160000Z
DTEND;VALUE=DATE-TIME:20210204T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/13
DESCRIPTION:Title:
Sylow Branching Coefficients and a Conjecture of Malle and Navarro\nby
Eugenio Giannelli (Università di Firenze) as part of GOThIC - Ischia Onl
ine Group Theory Conference\n\n\nAbstract\nLet $G$ be a finite group and l
et $P$ be a Sylow subgroup of $G$.\n\nIn 2012 Malle and Navarro conjecture
d that $P$ is normal in $G$ if and only if the permutation character assoc
iated to the natural action of $G$ on the cosets of $P$ has some specific
structural properties. In recent joint work with Law\, Long and Vallejo we
prove this conjecture. \n\nWe will start this talk by describing the prob
lem and its relevance in the context of representation theory of finite gr
oups. \n\nThen we will introduce and review some recent results on Sylow B
ranching Coefficients for symmetric groups.\n\nFinally we will talk about
the crucial role played by these objects in our proof of the conjecture.\n
LOCATION:https://researchseminars.org/talk/GOThIC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mima Stanojkovski (Max-Planck-Institut Leipzig)
DTSTART;VALUE=DATE-TIME:20210121T160000Z
DTEND;VALUE=DATE-TIME:20210121T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/14
DESCRIPTION:Title:
On the modular isomorphism problem for groups of class $3$\nby Mima St
anojkovski (Max-Planck-Institut Leipzig) as part of GOThIC - Ischia Online
Group Theory Conference\n\n\nAbstract\nLet $G$ be a finite group and let
$R$ be a commutative ring. In 1940\, G.\nHigman asked whether the isomorph
ism type of $G$ is determined by its\ngroup ring $RG$. Although the Isomor
phism Problem has generally a negative\nanswer\, the Modular Isomorphism P
roblem (MIP)\, for $G$ a $p$-group and $R$ a\nfield of positive characteri
stic $p$\, is still open. Examples of $p$-groups\nfor which the (MIP) has
a positive solution are abelian groups\, groups\nof order dividing $2^9$ o
r $3^7$ or $p^5$\, certain groups of maximal class\,\netc.\n\nI will give
an overview of the history of the (MIP) and will present\nrecent joint wor
k with Leo Margolis for groups of nilpotency class $3$. In\nparticular\, o
ur results yield new families of groups of order $p^6$ and\n$p^7$ for whic
h the (MIP) has a positive solution and a new invariant for certain\n$2$-g
enerated groups of class $3$.\n
LOCATION:https://researchseminars.org/talk/GOThIC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iker de las Heras Kerejeta (University of the Basque Country)
DTSTART;VALUE=DATE-TIME:20210128T160000Z
DTEND;VALUE=DATE-TIME:20210128T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/15
DESCRIPTION:Title:
Hausdorff dimension and Hausdorff spectra in profinite groups\nby Iker
de las Heras Kerejeta (University of the Basque Country) as part of GOThI
C - Ischia Online Group Theory Conference\n\n\nAbstract\nThe Hausdorff dim
ension is a generalisation of the usual concept of dimension which allows
to define the dimension of fractal sets in metric spaces. In the last deca
des\, this notion has led to fruitful applications in the context of count
ably based profinite groups\, as these groups can be naturally seen as met
ric spaces with respect to a given filtration series.\n\nIn this talk we w
ill give a brief introduction to this topic and we will overview some of t
he main related properties. Finally\, we will present some results concern
ing the so-called (normal) Hausdorff spectra of a given profinite group\,
which reflect the range of Hausdorff dimensions of closed (normal) subgrou
ps.\n\nJoint work with Benjamin Klopsch and Anitha Thillaisundaram.\n
LOCATION:https://researchseminars.org/talk/GOThIC/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kıvanç Ersoy (Freie Universität Berlin)
DTSTART;VALUE=DATE-TIME:20210211T160000Z
DTEND;VALUE=DATE-TIME:20210211T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/16
DESCRIPTION:Title:
On the centralizer depth in simple locally finite groups\nby Kıvanç
Ersoy (Freie Universität Berlin) as part of GOThIC - Ischia Online Group
Theory Conference\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOThIC/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norberto Gavioli (Università degli Studi dell'Aquila)
DTSTART;VALUE=DATE-TIME:20210218T160000Z
DTEND;VALUE=DATE-TIME:20210218T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/17
DESCRIPTION:Title:
Thin subalgebras of Lie algebras of maximal class\nby Norberto Gavioli
(Università degli Studi dell'Aquila) as part of GOThIC - Ischia Online G
roup Theory Conference\n\n\nAbstract\nJoint work with M. Avitabile\, A. Ca
ranti\, V. Monti\, M. F. Newman and E. O'Brien\n\nLet $L$ be an infinite d
imensional Lie algebra which is graded over the positive integers and is g
enerated by its first homogeneous component $L_1$. The algebra $L$ is of m
aximal class if $\\dim(L_1)=2$ and $\\dim(L_i)=1$ for $1$ larger than $1$.
The algebra $L$ is thin if it is not of maximal class\, $\\dim(L_1)=2$ an
d $L_{i+1}=[x\,L_1]$ for any nontrivial element $x$ in $L_i$.\n\nSuppose t
hat $E$ is a quadratic extension of a field $F$ and that $M$ is a Lie alge
bra of maximal class over $E$. We consider the Lie algebra $L$ generated o
ver the field $F$ by an $F$-subspace $L_1$ of $M_1$ having dimension $2$ o
ver $F$. We give necessary and sufficient conditions for the lie algebra $
L$ to be a thin graded $F$-subalgebra of the $F$-algebra $M$. We show also
that there are uncountably many such thin algebras that can be constructe
d by way of this “recipe”\, attaining the maximum possible cardinality
.\n\nThe authors started this project almost independently since 1999 and
their partial results have been luckily and duly recorded by A. Caranti. O
nly recently we have been able to develop together thorough and concise re
sults for this research.\n
LOCATION:https://researchseminars.org/talk/GOThIC/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Bier (Silesian University of Technology)
DTSTART;VALUE=DATE-TIME:20210225T160000Z
DTEND;VALUE=DATE-TIME:20210225T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/18
DESCRIPTION:Title:
On weak Sierpinski subsets in groups\nby Agnieszka Bier (Silesian Univ
ersity of Technology) as part of GOThIC - Ischia Online Group Theory Confe
rence\n\n\nAbstract\nA subset $E$ in a group $G$ is called a weak Sierpins
ki subset if for some $g\, h$ in $G$ and $a$ different from $b$ in $E$\, w
e have $gE = E \\setminus \\{a\\}$ and $hE = E \\setminus \\{b\\}$. In the
talk we discuss the subgroup generated by $g$ and $h$\, and show that eit
her it is free over $(g\,h)$ or it has presentation $G(k)=\\left\\langle
g\, h \\mid (h^{-1}g)^k \\right\\rangle$. We also characterize all weak Si
erpinski subsets in the groups $G(k)$. This is joint work with Y. Cornulie
r and P. Slanina.\n
LOCATION:https://researchseminars.org/talk/GOThIC/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Acciarri (Universidade de Brasília)
DTSTART;VALUE=DATE-TIME:20210304T160000Z
DTEND;VALUE=DATE-TIME:20210304T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/19
DESCRIPTION:Title:
A stronger version of Neumann’s BFC-theorem\nby Cristina Acciarri (U
niversidade de Brasília) as part of GOThIC - Ischia Online Group Theory C
onference\n\n\nAbstract\nA celebrated theorem of B. H. Neumann states that
if $G$ is a group in which all conjugacy classes are finite with bounded
size\, then the derived group $G’$ is finite. \n\nIn this talk we will d
iscuss a stronger version of Neumann’s result and some corollaries for f
inite and profinite groups. Based on a joint work with Pavel Shumyatsky.\n
LOCATION:https://researchseminars.org/talk/GOThIC/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunter Malle (Technische Universität Kaiserslautern)
DTSTART;VALUE=DATE-TIME:20210311T160000Z
DTEND;VALUE=DATE-TIME:20210311T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/20
DESCRIPTION:Title:
Conjugacy class numbers and $\\pi$-subgroups\nby Gunter Malle (Technis
che Universität Kaiserslautern) as part of GOThIC - Ischia Online Group T
heory Conference\n\n\nAbstract\nWe will discuss relations between the numb
er of conjugacy classes of a finite group and that of proper subgroups. On
the way\, we'll encounter the so-called almost abelian groups (a term coi
ned by J. Thompson). We then connect this to obtaining estimates for the
number of Brauer characters in a Brauer block of a finite group. This is j
oint work with Gabriel Navarro and Geoffrey Robinson.\n
LOCATION:https://researchseminars.org/talk/GOThIC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Britta Spaeth (Bergische Universität Wuppertal)
DTSTART;VALUE=DATE-TIME:20210318T160000Z
DTEND;VALUE=DATE-TIME:20210318T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/21
DESCRIPTION:Title:
Representation Theory above Spin Groups - Another Step towards the McKay C
onjecture\nby Britta Spaeth (Bergische Universität Wuppertal) as part
of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nIn the r
epresentation theory of finite groups it is suspected that the representat
ion theory of a group is already determined by its local subgroups. This l
ead to numerous conjectures like the McKay conjecture. During the last dec
ade substantial progress in a final proof of the McKay conjecture has been
made. After an overview of the development I sketch the open questions\,
that are mainly regarding the representation theory of spin groups and som
e progress made on one of those questions.\n
LOCATION:https://researchseminars.org/talk/GOThIC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas M. Keller (Texas State University)
DTSTART;VALUE=DATE-TIME:20210422T150000Z
DTEND;VALUE=DATE-TIME:20210422T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/22
DESCRIPTION:Title:
Character degrees\, conjugacy class sizes\, and element orders: three prim
es\nby Thomas M. Keller (Texas State University) as part of GOThIC - I
schia Online Group Theory Conference\n\n\nAbstract\nThere are many results
that give information on the structure\nof a finite group in terms of pro
perties that refer to its character degrees/\nclass sizes/element orders a
nd at most two primes. In this talk we present\na first attempt to extend
some of these results considering three primes. We concentrate on bounds f
or the Fitting height of solvable groups. (This is joint \nwork with Alex
Moreto.)\n
LOCATION:https://researchseminars.org/talk/GOThIC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Various (Various)
DTSTART;VALUE=DATE-TIME:20210325T160000Z
DTEND;VALUE=DATE-TIME:20210325T225900Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/23
DESCRIPTION:Title:
24 Hours of Ischia Group Theory\nby Various (Various) as part of GOThI
C - Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOThIC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Various (Various)
DTSTART;VALUE=DATE-TIME:20210325T230000Z
DTEND;VALUE=DATE-TIME:20210326T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/24
DESCRIPTION:Title:
24 Hours of Ischia Group Theory\nby Various (Various) as part of GOThI
C - Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOThIC/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eamonn O'Brien (The University of Auckland)
DTSTART;VALUE=DATE-TIME:20210415T090000Z
DTEND;VALUE=DATE-TIME:20210415T100000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/25
DESCRIPTION:Title:
Constructing composition factors for linear groups\nby Eamonn O'Brien
(The University of Auckland) as part of GOThIC - Ischia Online Group Theor
y Conference\n\n\nAbstract\nA recent result of Holt\, Leedham-Green and O'
Brien shows that we are\nfinally in a position where\, subject to certain
assumptions\, we\ncan construct in polynomial time the composition factors
of a\nsubgroup of $\\mathrm{GL}(d\, q)$. The principal components are "c
onstructive recognition" and presentations on "standard generators" for th
e finite simple groups. We survey this work.\n
LOCATION:https://researchseminars.org/talk/GOThIC/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Plotkin (Bar-Ilan University)
DTSTART;VALUE=DATE-TIME:20210429T150000Z
DTEND;VALUE=DATE-TIME:20210429T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/26
DESCRIPTION:Title:
Rigid logical characterizations of linear and Kac-Moody groups\nby Evg
eny Plotkin (Bar-Ilan University) as part of GOThIC - Ischia Online Group
Theory Conference\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOThIC/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Maslova (Russian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210506T150000Z
DTEND;VALUE=DATE-TIME:20210506T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/27
DESCRIPTION:Title:
On pronormality of subgroups of odd index in finite groups\nby Natalia
Maslova (Russian Academy of Sciences) as part of GOThIC - Ischia Online G
roup Theory Conference\n\n\nAbstract\nIn this talk we discuss a recent pro
gress in research of pronormality of subgroups of odd index in finite grou
ps.\n\nA subgroup $H$ of a group $G$ is pronormal in $G$ if for any elemen
t $g$ from $G$\, subgroups $H$ and $H^g$ are conjugate in the subgroup $\\
langle H\, H^g \\rangle$ generated by $H$ and $H^g$. Some problems in Fini
te Group Theory\, Combinatorics\, and Permutation Group Theory were solved
in terms of pronormality (see\, for example\, remarkable results by L. Ba
bai\, P. Palfy\, Ch. Praeger\, and others). Thus\, the question of descrip
tion of families of pronormal subgroups in finite groups is of interest. W
ell-known examples of pronormal subgroups in finite groups are normal subg
roups\, maximal subgroups\, Sylow subgroups\, Carter subgroups\, Hall subg
roups of solvable groups\, and so on.\n\nIn 2012\, E.P. Vdovin and D.O. Re
vin proved that the Hall subgroups are pronormal in finite simple groups a
nd conjectured that the subgroups of odd index are pronormal in finite sim
ple groups. This conjecture was disproved by A.S. Kondrat'ev\, the speaker
\, and D. Revin in 2016. However\, in many finite simple groups the subgro
ups of odd index are pronormal. Moreover\, the question of pronormality of
a subgroup of odd index in an arbitrary finite group can be partially red
uced to questions of pronormality of some subgroups of odd indices in its
chief factors.\n\nThis talk is partially based on joint results with S. Gl
asby\, A.S. Kondrat’ev\, C.E. Praeger\, and D.O. Revin.\n
LOCATION:https://researchseminars.org/talk/GOThIC/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Bartholdi (Georg-August Universität zu Göttingen)
DTSTART;VALUE=DATE-TIME:20210513T150000Z
DTEND;VALUE=DATE-TIME:20210513T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/28
DESCRIPTION:Title:
Dimension series and homotopy groups of spheres\nby Laurent Bartholdi
(Georg-August Universität zu Göttingen) as part of GOThIC - Ischia Onlin
e Group Theory Conference\n\n\nAbstract\nThe lower central series of a gro
up $G$ is defined by $\\gamma_1=G$ and $\\gamma_n = [G\,\\gamma_{n-1}]$. T
he "dimension series"\, introduced by Magnus\, is defined using the group
algebra over the integers: $$\\delta_n = \\{g: g-1\\text{ belongs to the $
n$-th power of the augmentation ideal}\\}.$$\n\nIt has been\, for the last
80 years\, a fundamental problem of group theory to relate these two seri
es. One always has $\\delta_n\\ge\\gamma_n$\, and a conjecture by Magnus\,
with false proofs by Cohn\, Losey\, etc.\, claims that they coincide\; bu
t Rips constructed an example with $\\delta_4/\\gamma_4$ cyclic of order 2
. On the positive side\, Sjogren showed that $\\delta_n/\\gamma_n$ is alwa
ys a torsion group\, of exponent bounded by a function of $n$. Furthermore
\, it was believed (and falsely proven by Gupta) that only $2$-torsion may
occur.\n\nIn joint work with Roman Mikhailov\, we prove however that ever
y torsion abelian group may occur as a quotient $\\delta_n/\\gamma_n$\; th
is proves that Sjogren's result is essentially optimal.\n\nEven more inter
estingly\, we show that this problem is intimately connected to the homoto
py groups $\\pi_n^(S^m)$ of spheres\; more precisely\, the quotient $\\del
ta_n/\\gamma_n$ is related to the difference between homotopy and homology
. We may explicitly produce $p$-torsion elements starting from the order-$
p$ element in the homotopy group $\\pi_{2p}(S^2)$ due to Serre.\n
LOCATION:https://researchseminars.org/talk/GOThIC/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Péter Pál Pálfy (Hungarian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210527T150000Z
DTEND;VALUE=DATE-TIME:20210527T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/29
DESCRIPTION:Title:
Galois and PSL\nby Péter Pál Pálfy (Hungarian Academy of Sciences)
as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nI
n his "testamentary letter" Galois claims\n(without proof) that $\\text{PS
L}(2\,p)$ does not have a subgroup of index $p$\nwhenever $p>11$\, and giv
es examples that for $p = 5\, 7\, 11$ such subgroups\nexist. \n\nThe attem
pt by Betti in 1853 to give a proof does not seem to be\ncomplete. Jordan'
s proof in his 1870 book uses methods certainly not\nknown to Galois. Nowa
days we deduce Galois's result from the complete\nlist of subgroups of $\\
text{PSL}(2\,p)$ obtained by Gierster in 1881.\n\nIn the talk I will give
a proof that might be close to Galois's own\nthoughts. \n\nLast October I
exchanged a few e-mails on this topic with\nPeter M. Neumann. So the talk
is in some way a commemoration of him.\n
LOCATION:https://researchseminars.org/talk/GOThIC/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John S. Wilson (Cambridge and Leipzig)
DTSTART;VALUE=DATE-TIME:20210603T150000Z
DTEND;VALUE=DATE-TIME:20210603T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/30
DESCRIPTION:Title:
A first-order perspective on finite groups\nby John S. Wilson (Cambrid
ge and Leipzig) as part of GOThIC - Ischia Online Group Theory Conference\
n\n\nAbstract\nThe finite axiomatizability of classes of finite groups\, a
nd the definability of naturally occurring subgroups\, have attracted cons
iderable attention. In this talk\, some of the results\, positive and def
inite\, will be discussed\, and it will be shown that the strikingly diffe
rent behaviour of certain properties seems to be reflected in (non-first-o
rder) studies of these properties.\n
LOCATION:https://researchseminars.org/talk/GOThIC/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Skipper (Ohio State University)
DTSTART;VALUE=DATE-TIME:20210610T150000Z
DTEND;VALUE=DATE-TIME:20210610T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/31
DESCRIPTION:Title:
The Cantor-Bendixson rank of the Grigorchuk group\nby Rachel Skipper (
Ohio State University) as part of GOThIC - Ischia Online Group Theory Conf
erence\n\n\nAbstract\nThe space of subgroups of a group has a natural Poli
sh topology and understanding this space can help to understand the group.
In this talk\, we will consider the Cantor-Bendixson derivative and rank
for the space of subgroups of the Grigorchuk group\, using it to stratify
the subgroups of this group. This is a joint work with Phillip Wesolek.\n
LOCATION:https://researchseminars.org/talk/GOThIC/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Weigel (Università di Milano Bicocca)
DTSTART;VALUE=DATE-TIME:20210520T150000Z
DTEND;VALUE=DATE-TIME:20210520T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/32
DESCRIPTION:Title:
Maximal pro $p$-quotients of absolute Galois groups\nby Thomas Weigel
(Università di Milano Bicocca) as part of GOThIC - Ischia Online Group Th
eory Conference\n\n\nAbstract\n(Joint work with Claudio Quadrelli.)\n\nIt
is well-known that the absolute Galois group $G_K = \\operatorname{Gal}(\\
bar K^{\\text{sep}}/K)$ of a field $K$\nis a profinite group. However\, on
ly in very restrictive circumstances it is possible to\nanalyze the struct
ure of $G_K$ completely. A first approximation - which is untertaken\nfreq
uently - is to investigate the maximal pro-$p$ quotient $G_K(p) = G_K/O^{p
}\n(G_K)$ for a prime $p$. Here $O_p(\\_)$ is the closed subgroup being ge
nerated by all Sylow\npro-$\\ell$ subgroups for $\\ell \\ne p$. The absolu
te Galois group $G_K$ comes equipped with a\ncontinuous group homomorphism
\n$$\n\\theta_{K\,p} : G_K \\to \\mathbb{Z}_p^{x}\n\,$$\nthe $p$-cyclotomi
c character\, where $\\mathbb{Z}_p^{x}$ denotes group of the invertible el
ements in\nthe ring of $p$-adic integers $\\mathbb{Z}_p$. In case that $K$
contains a primitive $p$-th root of unity\,\nthe homomorphism $\\theta_{K
\,p}$ is induced from a group homomorphism\n$$\n\\hat\\theta_{K\,p} : G_K(
p) \\to \\mathbb{Z}_p^{x}\n.$$\n\nA pro-$p$ group $G$ together with a cont
inuous group homomorphism $\\theta : G → \\mathbb{Z}_p^{x}$\nis\nalso ca
lled an oriented pro-$p$ group. Although the structure of $G_K(p)$ is in g
eneral\nmuch easier to analyze than $G_K$ there are still many open questi
ons concerning\nthe oriented pro-$p$ groups $(G_K(p)\, \\hat\\theta_{K\,p}
)$. E.g.\, around 25 years ago it was conjectured by I. Efrat\, that in ca
se that $G_K(p)$ is a finitely generated pro-$p$ group\,\nthen $(G_K(p)\,
\\hat\\theta_{K\,p})$ must be of elementary type. Here one defines the cla
ss of oriented pro-$p$ groups of elementary type as the smallest class of
oriented pro-$p$ groups\nwhich is closed under free products\, and fibre p
roducts with $\\theta$-abelian oriented pro-$p$ groups which contains $(F\
, \\alpha)$ for all finitely generated free pro-$p$ groups $F$ and any $\\
alpha : F \\to \\mathbb{Z}_p^{x}$\, as well as $(D\, \\eth)$ for all Demus
h’kin pro-$p$ groups $D$\, where $\\eth: D \\to \\mathbb{Z}_p^{x}$ is th
e $p$-orientation induced by the dualizing module of D. In the talk I will
discuss recent developments in Field theory\, which transformed I. Efrat
’s elementary\ntype conjecture into a purely group theoretic question. R
ecently\, this question\nhas been investigated successfully for certain cl
asses of oriented pro-$p$ groups: 1)\nRight-angled Artin pro-$p$ groups wi
th trivial orientation (I. Snopce\, P. Zalesskii)\,\n2) Generalized right-
angled Artin pro-$p$ groups (S. Blumer\, C. Quadrelli\, T.W.).\n
LOCATION:https://researchseminars.org/talk/GOThIC/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Camina (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210701T150000Z
DTEND;VALUE=DATE-TIME:20210701T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/33
DESCRIPTION:Title:
Word problems for finite nilpotent groups\nby Rachel Camina (Universit
y of Cambridge) as part of GOThIC - Ischia Online Group Theory Conference\
n\n\nAbstract\nWe consider word maps on finite nilpotent groups and count
the sizes of the fibres for elements in the image. We consider Amit’s co
njecture and its generalisation\, which say that these fibres should have
size at least $\\lvert G \\rvert^{k−1}$\, where the word is on $k$ varia
bles. This is joint work with Ainhoa Iñiguez and Anitha Thillaisundaram.\
n
LOCATION:https://researchseminars.org/talk/GOThIC/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (University of Münster)
DTSTART;VALUE=DATE-TIME:20210708T150000Z
DTEND;VALUE=DATE-TIME:20210708T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/34
DESCRIPTION:Title:
Kaplansky's conjectures\nby Giles Gardam (University of Münster) as p
art of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nThree
conjectures on group rings of torsion-free groups are commonly attributed
to Kaplansky\, namely the unit\, zero divisor and idempotent conjectures.
For example\, the zero divisor conjecture predicts that if $K$ is a field
and $G$ is a torsion-free group\, then the group ring $K[G]$ has no zero
divisors. I will survey what is known about the conjectures\, including th
eir relationships to each other and to other conjectures and group propert
ies\, and present my recent counterexample to the unit conjecture.\n
LOCATION:https://researchseminars.org/talk/GOThIC/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Segal (University of Oxford)
DTSTART;VALUE=DATE-TIME:20210617T150000Z
DTEND;VALUE=DATE-TIME:20210617T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/35
DESCRIPTION:Title:
Groups\, Rings\, Logic\nby Dan Segal (University of Oxford) as part of
GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nIn group th
eory\, interesting statements about a group usually can’t be ex-\npresse
d in the language of first-order logic. It turns out\, however\, that some
\ngroups can actually be determined by their first-order properties\, or\,
even more\nstrongly\, by a single first-order sentence. In the latter cas
e the group is said to\nbe finitely axiomatizable.\n\nI will describe some
examples of this phenomenon (joint work with A. Nies\nand K. Tent). One f
amily of results concerns axiomatizability of $p$-adic analytic\npro-$p$ g
roups\, within the class of all profinite groups.\n\nAnother main result i
s that for an adjoint simple Chevalley group of rank at\nleast $2$ and an
integral domain $R$\, the group $G(R)$ is bi-interpretable with the\nring
$R$. This means in particular that first-order properties of the group $G(
R)$\ncorrespond to first-order properties of the ring $R$. As many rings a
re known to\nbe finitely axiomatizable we obtain the corresponding result
for many groups\;\nthis holds in particular for every finitely generated g
roup of the form $G(R)$.\n
LOCATION:https://researchseminars.org/talk/GOThIC/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Nikolov (University of Oxford)
DTSTART;VALUE=DATE-TIME:20210624T150000Z
DTEND;VALUE=DATE-TIME:20210624T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/36
DESCRIPTION:Title:
On profinite groups with positive rank gradient\nby Nikolay Nikolov (U
niversity of Oxford) as part of GOThIC - Ischia Online Group Theory Confer
ence\n\n\nAbstract\nIn this talk I will introduce rank gradient of groups
and discuss open questions about groups with positive rank gradient. In th
e second part I will focus on the profinite situation and sketch a proof t
hat a profinite group $G$ with positive rank gradient does not satisfy a g
roup law.\n
LOCATION:https://researchseminars.org/talk/GOThIC/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cindy (Sin Yi) Tsang (Ochanomizu University)
DTSTART;VALUE=DATE-TIME:20210715T130000Z
DTEND;VALUE=DATE-TIME:20210715T140000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/37
DESCRIPTION:Title:
The multiple holomorph of centerless groups\nby Cindy (Sin Yi) Tsang (
Ochanomizu University) as part of GOThIC - Ischia Online Group Theory Conf
erence\n\n\nAbstract\nThe holomorph $\\operatorname{Hol}(G)$ of a group $G
$ may be defined as the normalizer of the subgroup of left translations in
the group of all permutations of $G$. The multiple holomorph $\\operatorn
ame{NHol}(G)$ of $G$ may in turn be defined as the normalizer of the holom
orph. Their quotient $T(G) = \\operatorname{NHol}(G)/\\operatorname{Hol}(G
)$ has been computed for various families of groups G\, and interestingly
$T(G)$ turns out to be elementary $2$-abelian in many of the known cases.
In this talk\, we consider the case when $G$ is centerless\, and we will p
resent our new result that $T(G)$ has to be elementary $2$-abelian unless
G satisfies some fairly strong conditions. For example\, our result implie
s that T(G) is elementary $2$-abelian when $G$ is any (not necessarily fin
ite) centerless perfect/almost simple/complete group.\n
LOCATION:https://researchseminars.org/talk/GOThIC/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Zalesski (University of Brasilia)
DTSTART;VALUE=DATE-TIME:20210722T150000Z
DTEND;VALUE=DATE-TIME:20210722T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/38
DESCRIPTION:Title:
Finitely generated pro-$p$ groups acting on pro-$p$ trees\nby Pavel Za
lesski (University of Brasilia) as part of GOThIC - Ischia Online Group Th
eory Conference\n\n\nAbstract\nI shall discuss various results on splittin
g of a pro-$p$ group as a free amalgamated pro-$p$ product or HNN-extensio
n in the spirit of the Bass-Serre theory of groups acting on trees.\n
LOCATION:https://researchseminars.org/talk/GOThIC/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Guralnick (University of Southern California)
DTSTART;VALUE=DATE-TIME:20211014T150000Z
DTEND;VALUE=DATE-TIME:20211014T160000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/40
DESCRIPTION:Title:
Topological Generation of Algebraic Groups\nby Robert Guralnick (Unive
rsity of Southern California) as part of GOThIC - Ischia Online Group Theo
ry Conference\n\n\nAbstract\nWe consider the problem of generation of (mos
tly simple) algebraic groups $G$ in the topological setting using the Zari
ski topology. In particular\, we will discuss the problem of how many conj
ugates of a given element are needed. We will give applications to some ge
neration problems for finite groups of Lie type and to generic stabilizers
.\n\nThis is joint work with Tim Burness and Spencer Gerhardt.\n
LOCATION:https://researchseminars.org/talk/GOThIC/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ángel del Río (Universidad de Murcia)
DTSTART;VALUE=DATE-TIME:20211021T160000Z
DTEND;VALUE=DATE-TIME:20211021T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/41
DESCRIPTION:Title:
A negative solution to the Modular Isomorphism Problem\nby Ángel del
Río (Universidad de Murcia) as part of GOThIC - Ischia Online Group Theor
y Conference\n\n\nAbstract\nLet $R$ be a ring. \nThe Isomorphism Problem f
or group rings over $R$ asks whether the isomorphism type of a group $G$ i
s determined by the isomorphism type of the group ring $RG$. \nThe special
case where $R$ is a field with $p$ elements and $G$ is a finite $p$-group
\, for $p$ prime\, is known as the Modular Isomorphism Problem. \n\nThe hi
story of the Isomorphism Problem goes back to a seminal paper of G. Higman
in the 1940s. The Modular Isomorphism Problem appeared in a survey paper
by R. Brauer in 1963. While many relevant instances of the general Isomorp
hism Problem have been already resolved\, the Modular Isomorphism Problem
resisted until now. \n\nIn cooperation with Diego García and Leo Margolis
we discovered recently two non-isomorphic groups of order $2^9$ whose gro
up algebras over any field of characteristic $2$ are isomorphic. We will p
resent this example and give an overview of the state of the art on the Is
omorphism Problem.\n
LOCATION:https://researchseminars.org/talk/GOThIC/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele D'Angeli (Università Niccolò Cusano\, Roma))
DTSTART;VALUE=DATE-TIME:20211028T160000Z
DTEND;VALUE=DATE-TIME:20211028T170000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/42
DESCRIPTION:Title:
Graph Automaton Groups\nby Daniele D'Angeli (Università Niccolò Cusa
no\, Roma)) as part of GOThIC - Ischia Online Group Theory Conference\n\n\
nAbstract\nIn this talk I will review some basic and interesting propertie
s of automaton groups\, i.e. groups generated by the action of a transduce
r on a finite alphabet. Then I will explain a new construction (introduced
in collaboration with M. Cavaleri\, A. Donno and E. Rodaro) to obtain aut
omaton groups starting from finite graphs. This class of "Graph Automaton
groups" contains classic examples of automaton groups and other groups exh
ibiting interesting combinatorial and spectral properties.\n
LOCATION:https://researchseminars.org/talk/GOThIC/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Vaughan-Lee (Christ Church\, Oxford)
DTSTART;VALUE=DATE-TIME:20211104T170000Z
DTEND;VALUE=DATE-TIME:20211104T180000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/43
DESCRIPTION:Title:
Schur’s exponent conjecture\nby Michael Vaughan-Lee (Christ Church\,
Oxford) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAb
stract\nIf $G$ is a finite group and we write $G = F/R$ where $F$ is a fre
e group\,\nthen the Schur multiplier $M(G)$ is $(R \\cap F')/[F\, R]$.\n\n
There is a long-standing conjecture attributed to I. Schur that the expone
nt of $M(G)$ divides the exponent of $G$. It is easy to show that this is
true\nfor groups $G$ of exponent $2$ or exponent $3$\, but it has been kno
wn since 1974\nthat the conjecture fails for exponent $4$. However the tru
th or otherwise of\nthis conjecture has remained open up till now for grou
ps of odd exponent.\n\nIn my talk I describe counterexamples to the conjec
ture of exponent $5$\nand exponent $9$.\n\nI also give some suggestions fo
r further counterexamples\, and explore the\npossibilities for alternative
conjectures.\n
LOCATION:https://researchseminars.org/talk/GOThIC/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Franchi (Università Cattolica del Sacro Cuore\, Brescia)
DTSTART;VALUE=DATE-TIME:20211111T170000Z
DTEND;VALUE=DATE-TIME:20211111T180000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/44
DESCRIPTION:Title:
Majorana representations of finite groups\nby Clara Franchi (Universit
à Cattolica del Sacro Cuore\, Brescia) as part of GOThIC - Ischia Online
Group Theory Conference\n\n\nAbstract\nThe concept of Majorana representat
ions of finite groups have been introduced by A.A. Ivanov in 2009 as a too
l to better understand the Monster and its representation on the Conway-No
rton-Griess algebra. \n\nIn my talk I will review the principal results of
the theory of Majorana representations of finite groups. In particular\,
I will focus on the representations of the symmetric groups\, presenting
some joint work with A.A. Ivanov and M. Mainardis.\n
LOCATION:https://researchseminars.org/talk/GOThIC/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandra Garrido (Universidad Autónoma de Madrid)
DTSTART;VALUE=DATE-TIME:20211202T170000Z
DTEND;VALUE=DATE-TIME:20211202T180000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/45
DESCRIPTION:Title:
On various profinite completions of groups acting on rooted trees\nby
Alejandra Garrido (Universidad Autónoma de Madrid) as part of GOThIC - Is
chia Online Group Theory Conference\n\n\nAbstract\nGroups that act faithfu
lly on rooted trees can be studied via their finite quotients. There are s
everal natural collections of finite quotients that can be chosen for this
. The mathematical object that encodes all these finite quotients and the
maps between them is the profinite completion of the group (with respect t
o the chosen collection). Taking all possible finite quotients of the grou
p gives *the* profinite completion of the group\, annd this maps onto each
of the other completions. Determining the kernels of these maps is known
as the congruence subgroup problem. This has been studied by various aut
hors over the last few years\, most notably for self-similar groups and (w
eakly) branch groups. In the case of self-similar regular branch groups\,
much insight can be gained into this problem using a symbolic-dynamical po
int of view. After reviewing the problem and previous work on it\, I will
report on work in progress with Zoran Sunic on determining the dynamical c
omplexity of these completions and calculating some of these kernels with
relative ease.\n\nExamples will be given. No previous knowledge of profini
te\, self-similar or branch groups is required.\n
LOCATION:https://researchseminars.org/talk/GOThIC/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viji Thomas (Indian Institute of Science Education and Research Th
iruvananthapuram)
DTSTART;VALUE=DATE-TIME:20211118T170000Z
DTEND;VALUE=DATE-TIME:20211118T180000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/46
DESCRIPTION:Title:
Schur’s exponent conjecture and related problems\nby Viji Thomas (In
dian Institute of Science Education and Research Thiruvananthapuram) as pa
rt of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nAssume
$G$ is a finite $p$-group\, and let $S$ be a Sylow $p$-subgroup of $\\ope
ratorname{Aut}(G)$ with $\\operatorname{exp}(S) = q$. We\nprove that if $G
$ is of class at most $p^{2} − 1$\, then $\\operatorname{exp}(G) \\mid p
^{2}\nq^{3}$\, and if $G$ is a metabelian $p$-group of class\nat most $2 p
− 1$\, then $\\operatorname{exp}(G) \\mid p q^{3}$. To obtain this resu
lt\, we will first speak about Schur’s exponent conjecture and related p
roblems. This is joint work with my PhD student P. Komma.\n
LOCATION:https://researchseminars.org/talk/GOThIC/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Dolores Pérez-Ramos (University of Valencia)
DTSTART;VALUE=DATE-TIME:20211209T170000Z
DTEND;VALUE=DATE-TIME:20211209T180000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/47
DESCRIPTION:by M. Dolores Pérez-Ramos (University of Valencia) as part of
GOThIC - Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOThIC/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Mattarei (University of Lincoln)
DTSTART;VALUE=DATE-TIME:20211125T170000Z
DTEND;VALUE=DATE-TIME:20211125T180000Z
DTSTAMP;VALUE=DATE-TIME:20211209T072614Z
UID:GOThIC/48
DESCRIPTION:by Sandro Mattarei (University of Lincoln) as part of GOThIC -
Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GOThIC/48/
END:VEVENT
END:VCALENDAR