# On some modules over group rings of locally soluble groups with rank restrictions on subgroups

Author O. Yu. Dashkova
odashkova@yandex.ru
Dnipropetrovsk National University

Abstract The author studies an $\bf R$$G$-module $A$ such that $\bf R$ is an integral domain, $G$ is a locally soluble group of infinite section $p$-rank (or infinite 0-rank), $C_{G}(A)=1$, $A/C_{A}(G)$ is not a noetherian $\bf R$-module, and for every proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank respectively), the quotient module $A/C_{A}(H)$ is a noetherian $\bf R$-module. It is proved that under the above conditions, $G$ is a soluble group. Some properties of soluble groups of this type are obtained.
Keywords noetherian $R$-module; locally soluble group; group ring
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Pages 119-127
Volume 36
Issue 2
Year 2011
Journal Matematychni Studii
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