Centralizers of subgroups in simple locally finite groups

ERSOY K., KUZUCUOĞLU M.

JOURNAL OF GROUP THEORY, vol.15, no.1, pp.9-22, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.1515/jgt.2010.087
  • Journal Name: JOURNAL OF GROUP THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.9-22
  • Middle East Technical University Affiliated: Yes

Abstract

Hartley asked the following question: Is the centralizer of every finite subgroup in a simple non-linear locally finite group infinite? We answer a stronger version of this question for finite K-semisimple subgroups. Namely let G be a non-linear simple locally finite group which has a Kegel sequence K = {(G(i), 1) : i is an element of N} consisting of finite simple subgroups. Then for any finite subgroup F consisting of K-semisimple elements in G, the centralizer C-G(F) has an infinite abelian subgroup A isomorphic to a direct product of Z(pi) for infinitely many distinct primes p(i).