Locally finite groups and their subgroups with small centralizers

Date

2017-07-01

Author

ERSOY, KIVANÇ
Kuzucuoğlu, Mahmut
Shunwatsky, Pavel

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Let p be a prime and G a locally finite group containing an elementary abelian p-subgroup A of rank at least 3 such that C-G(A) is Chernikov and C-G(a) involves no infinite simple groups for any a is an element of A(#). We show that G is almost locally soluble (Theorem 1.1). The key step in the proof is the following characterization of PSLp(k): An infinite simple locally finite group G admits an elementary abelian p-group of automorphisms A such that C-G(A) is Chernikov and C-G(A) Keywords: involves no infinite simple groups for any a is an element of A(#) if and only Locally finite group if G is isomorphic to PSLp(k) for some locally finite field k Centralizer of characteristic different from p and A has order p(2). (C) 2017 Published by Elsevier Inc.

Subject Keywords

Locally finite group, Centralizer

URI

https://hdl.handle.net/11511/48896

Journal

JOURNAL OF ALGEBRA

DOI

https://doi.org/10.1016/j.jalgebra.2017.02.018

Collections

Department of Mathematics, Article

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Citation Formats

K. ERSOY, M. Kuzucuoğlu, and P. Shunwatsky, “Locally finite groups and their subgroups with small centralizers,” JOURNAL OF ALGEBRA, pp. 1–11, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48896.