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 $$**Z**
be the ring of integers, $A$ be a $$**Z**G-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 $$**Z**G-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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k113/k11302h.htm

Last modified: May 4, 2012