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SUMMARY:Locally Finite Groups and Their Subgroups with Small Centralizers
DTSTART:20170519T101500
DTSTAMP:20260609T231223Z
UID:0968dbf64d13c9edb2ab8dc32cc313eb084349afe235a0f3bf01c531
CATEGORIES:Conferences - Seminars
DESCRIPTION:Kivanc Ersoy\, Kaiserslautern and Istanbul\nLet $p$ be a prime
  and $G$ a locally finite group containing an elementary abelian $p$-subgr
 oup $A$   of rank at least $3$ such that $C_{G}(A)$ is Chernikov (that i
 s\, a locally finite group satisfying minimal condition on subgroups) and 
 $C_{G}(a)$ involves no infinite simple groups for any $a\\in A*$. In this 
 talk\, we prove that G is almost locally soluble. To prove this result\, w
 e first give a\ncharacterization of $PSL_{p}(k)$:\n\nTheorem: An infinite 
 simple locally finite group $G$ admits an elementary abelian $p$-group of 
 automorphisms $A$   such that $C_{G}(A)$ is Chernikov and $C_{G}(a)$ inv
 olves no infinite simple groups for any $a\\in A^{\\sharp}$ if and only if
  $G$   is isomorphic to $PSL_{p}(k)$ for some locally finite field $k$ o
 f characteristic different from $p$ and $A$   has order $p^{2}$.\nThis i
 s a joint work with Mahmut Kuzucuoglu and Pavel Shumyatsky.\n\n 
LOCATION:GR A3 31
STATUS:CONFIRMED
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