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SUMMARY:Cindy (Sin Yi) Tsang (Ochanomizu University)
DTSTART:20210715T130000Z
DTEND:20210715T140000Z
DTSTAMP:20260423T053139Z
UID:GOThIC/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/37/">
 The multiple holomorph of centerless groups</a>\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/
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