FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 7, PAGES 113-125

On one class of modules that are close to Noetherian

O. Yu. Dashkova

Abstract

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We consider an $$RG-module $A$ over a commutative Noetherian ring $$R. Let $G$ be a group having infinite section $p$-rank (or infinite $0$-rank) such that $C$_G(A)=1, $A/C$_A(G) is not a Noetherian $$R-module, but the quotient $A/C$_A(H) is a Noetherian $$R-module for every proper subgroup $H$ of infinite section $p$-rank (or infinite $0$-rank, respectively). In this paper, it is proved that if $G$ is a locally soluble group, then $G$ is soluble. Some properties of soluble groups of this type are also obtained.

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Last modified: April 18, 2010