BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Colva Roney-Dougal (The University of St Andrews) DTSTART:20201008T150000Z DTEND:20201008T160000Z DTSTAMP:20260422T225821Z 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:20201015T150000Z DTEND:20201015T160000Z DTSTAMP:20260422T225821Z 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:20201022T150000Z DTEND:20201022T160000Z DTSTAMP:20260422T225821Z 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:20201029T160000Z DTEND:20201029T170000Z DTSTAMP:20260422T225821Z 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:20201105T160000Z DTEND:20201105T170000Z DTSTAMP:20260422T225821Z 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:20201112T160000Z DTEND:20201112T170000Z DTSTAMP:20260422T225821Z 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:20201119T160000Z DTEND:20201119T170000Z DTSTAMP:20260422T225821Z 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:20201126T160000Z DTEND:20201126T170000Z DTSTAMP:20260422T225821Z 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:20201203T160000Z DTEND:20201203T170000Z DTSTAMP:20260422T225821Z 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:20201210T160000Z DTEND:20201210T170000Z DTSTAMP:20260422T225821Z 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:20201217T160000Z DTEND:20201217T170000Z DTSTAMP:20260422T225821Z 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:20210114T150000Z DTEND:20210114T160000Z DTSTAMP:20260422T225821Z 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:20210204T160000Z DTEND:20210204T170000Z DTSTAMP:20260422T225821Z 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:20210121T160000Z DTEND:20210121T170000Z DTSTAMP:20260422T225821Z 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:20210128T160000Z DTEND:20210128T170000Z DTSTAMP:20260422T225821Z 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:20210211T160000Z DTEND:20210211T170000Z DTSTAMP:20260422T225821Z 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:20210218T160000Z DTEND:20210218T170000Z DTSTAMP:20260422T225821Z 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:20210225T160000Z DTEND:20210225T170000Z DTSTAMP:20260422T225821Z 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:20210304T160000Z DTEND:20210304T170000Z DTSTAMP:20260422T225821Z 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:20210311T160000Z DTEND:20210311T170000Z DTSTAMP:20260422T225821Z 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:20210318T160000Z DTEND:20210318T170000Z DTSTAMP:20260422T225821Z 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:20210422T150000Z DTEND:20210422T160000Z DTSTAMP:20260422T225821Z 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:20210325T160000Z DTEND:20210325T225900Z DTSTAMP:20260422T225821Z 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:20210325T230000Z DTEND:20210326T160000Z DTSTAMP:20260422T225821Z 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:20210415T090000Z DTEND:20210415T100000Z DTSTAMP:20260422T225821Z 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:20210429T150000Z DTEND:20210429T160000Z DTSTAMP:20260422T225821Z 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:20210506T150000Z DTEND:20210506T160000Z DTSTAMP:20260422T225821Z 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:20210513T150000Z DTEND:20210513T160000Z DTSTAMP:20260422T225821Z 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:20210527T150000Z DTEND:20210527T160000Z DTSTAMP:20260422T225821Z 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:20210603T150000Z DTEND:20210603T160000Z DTSTAMP:20260422T225821Z 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:20210610T150000Z DTEND:20210610T160000Z DTSTAMP:20260422T225821Z 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:20210520T150000Z DTEND:20210520T160000Z DTSTAMP:20260422T225821Z 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:20210701T150000Z DTEND:20210701T160000Z DTSTAMP:20260422T225821Z 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:20210708T150000Z DTEND:20210708T160000Z DTSTAMP:20260422T225821Z 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:20210617T150000Z DTEND:20210617T160000Z DTSTAMP:20260422T225821Z 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:20210624T150000Z DTEND:20210624T160000Z DTSTAMP:20260422T225821Z 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:20210715T130000Z DTEND:20210715T140000Z DTSTAMP:20260422T225821Z 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:20210722T150000Z DTEND:20210722T160000Z DTSTAMP:20260422T225821Z 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:20211014T150000Z DTEND:20211014T160000Z DTSTAMP:20260422T225821Z 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:20211021T160000Z DTEND:20211021T170000Z DTSTAMP:20260422T225821Z 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:20211028T160000Z DTEND:20211028T170000Z DTSTAMP:20260422T225821Z 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:20211104T170000Z DTEND:20211104T180000Z DTSTAMP:20260422T225821Z 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:20211111T170000Z DTEND:20211111T180000Z DTSTAMP:20260422T225821Z 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:20211202T170000Z DTEND:20211202T180000Z DTSTAMP:20260422T225821Z 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:20211118T170000Z DTEND:20211118T180000Z DTSTAMP:20260422T225821Z 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:20211209T170000Z DTEND:20211209T180000Z DTSTAMP:20260422T225821Z 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:20211125T170000Z DTEND:20211125T180000Z DTSTAMP:20260422T225821Z 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