Centralizers of subgroups in simple locally finite groups

Kuzucuoğlu, Mahmut
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).

Citation Formats
K. ERSOY and M. Kuzucuoğlu, “Centralizers of subgroups in simple locally finite groups,” JOURNAL OF GROUP THEORY, vol. 15, no. 1, pp. 9–22, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44423.