Centralizers of subgroups in simple locally finite groups

2012-01-01
ERSOY, KIVANÇ
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).
JOURNAL OF GROUP THEORY

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Citation Formats
K. ERSOY and M. Kuzucuoğlu, “Centralizers of subgroups in simple locally finite groups,” JOURNAL OF GROUP THEORY, pp. 9–22, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44423.