On some modules over group rings of locally soluble groups with rank restrictions on subgroups - O. Yu. Dashkova (Математичні Студії)
The author studies an $f R$$G$-module $A$ such that $f R$is an integral domain, $G$ is a locally soluble group ofinfinite section $p$-rank (or infinite 0-rank), $C_{G}(A)=1$,$A/C_{A}(G)$ is not a~noetherian $f R$-module, and for everyproper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank respectively), the quotient module $A/C_{A}(H)$ isa noetherian $f R$-module. It is proved that under the aboveconditions, $G$ is a soluble group. Some properties of solublegroups of this type are obtained.