This article is cited in 1 paper

RESEARCH ARTICLE

On locally soluble $AFN$-groups

Olga Yu. Dashkova

49055, Ukraine, Dnepropetrovsk, prospekt Kirova, 102-D, kv. 35

Abstract: Let $A$ be an $\mathbf{R}G$-module, where $\bf R$ is a commutative ring, $G$ is a locally soluble group, $C_{G}(A)=1$, and each proper subgroup $H$ of $G$ for which $A/C_{A}(H)$ is not a noetherian $\bf R$-module, is finitely generated. We describe the structure of a locally soluble group $G$ with these conditions and the structure of $G$ under consideration if $G$ is a finitely generated soluble group and the quotient module $A/C_{A}(G)$ is not a noetherian $\bf R$-module.

Keywords: locally soluble group, noetherian module, group ring.

MSC: 20F19

Received: 21.04.2012
Revised: 02.10.2012

Language: English

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