Locally finite groups and their subgroups with small centralizers


ERSOY K., KUZUCUOĞLU M. , Shunwatsky P.

JOURNAL OF ALGEBRA, vol.481, pp.1-11, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 481
  • Publication Date: 2017
  • Doi Number: 10.1016/j.jalgebra.2017.02.018
  • Title of Journal : JOURNAL OF ALGEBRA
  • Page Numbers: pp.1-11

Abstract

Let p be a prime and G a locally finite group containing an elementary abelian p-subgroup A of rank at least 3 such that C-G(A) is Chernikov and C-G(a) involves no infinite simple groups for any a is an element of A(#). We show that G is almost locally soluble (Theorem 1.1). The key step in the proof is the following characterization of PSLp(k): 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) Keywords: involves no infinite simple groups for any a is an element of A(#) if and only Locally finite group if G is isomorphic to PSLp(k) for some locally finite field k Centralizer of characteristic different from p and A has order p(2). (C) 2017 Published by Elsevier Inc.