FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 3, PAGES 25-37

Modules over integer group rings of locally soluble groups with minimax restriction

O. Yu. Dashkova

Abstract

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Let $$Z be the ring of integers, $A$ be a $$ZG-module, where $A/C$_A(G) is not a minimax $$Z-module, $C$_G(A) = 1, and $G$ is a locally soluble group. Let $L$_nm(G) be the system of all subgroups $H$£ G such that quotient modules $A/C$_A(H) are not minimax $$Z-modules. The author studies $$ZG-modules $A$ such that $L$_nm(G) satisfies the minimal condition as an ordered set. It is proved that a locally soluble group $G$ with these conditions is soluble. The structure of the group $G$ is described.

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Last modified: May 4, 2012