Centralizers of involutions in locally finite-simple groups

Berkman A., KUZUCUOĞLU M., OeZyurt E.

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, cilt.118, ss.189-196, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 118
  • Basım Tarihi: 2007
  • Dergi Adı: RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.189-196
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We consider infinite locally finite-simple groups (that is, infinite groups in which every finite subset lies in a finite simple subgroup). We first prove that in such groups, centralizers of involutions either are soluble or involve an infinite simple group, and we conclude that in either case centralizers of involutions are not inert subgroups. We also show that in such groups, the centralizer of an involution is linear if and only if the ambient group is linear.