On locally finite groups with a small centralizer of a four-subgroup

Abstract

The main result of the paper is the following theorem. Let G be a locally finite group having a four-subgroup V such that CG(V ) is finite. Suppose that V contains two involutions v1 and v2 such that the centralizers CG(v1) and CG(v2) have finite exponent. Then G is almost locally soluble and [G, V ] has finite exponent. Since [G, V ] has finite index in G, the result gives a fairly detailed information about the structure of G.Mathematics Subject Classification (2010). 20F50, 20E25.