Centralizers of subgroups in simple locally finite groups

ERSOY K., KUZUCUOĞLU M.

JOURNAL OF GROUP THEORY, cilt.15, sa.1, ss.9-22, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1515/jgt.2010.087
  • Dergi Adı: JOURNAL OF GROUP THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9-22
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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).