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

View as HTML
View as gif image

We consider an $$**R**G-module $A$ over a commutative
Noetherian ring $$**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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k097/k09704h.htm

Last modified: April 18, 2010