Modules over group rings of locally finite groups with finiteness restrictions

Dashkova, Olga (2017) Modules over group rings of locally finite groups with finiteness restrictions. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (1). pp. 23-29. ISSN 0866-0174

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Abstract

We study an RG-module A , where R is a ring, A/CA(G) is infinite, CG(A) = 1, G is a group. Let Lnf(G) be the system of all subgroups H ≤ G such that the quotient modules A/CA(H) are infinite. We investigate an RG-module A such that Lnf(G) satisfies either the weak minimal condition or the weak maximal condition as an ordered set. It is proved that if G is a locally finite group then either G is a Chernikov group or G is a finite-finitary group of automorphisms of A.

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