MMN-1240
Modules over group rings of locally soluble groups with a certain condition of minimality
O. YU. Dashkova;Abstract
Let $A$ be an $\bf R$$G$-module, where $\bf R$ is an associative ring, $A/C_{A}(G)$ is an infinite $\bf R$-module,
$C_{G}(A)=1$, $G$ is a locally soluble group. Let $L_{nf}(G)$ be the
system of all subgroups $H \leq G$ such that quotient modules
$A/C_{A}(H)$ are infinite $\bf R$-modules.
The author studies an $\bf R$$G$-module $A$ such that
$L_{nf}(G)$ 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 $G$ is described.
Vol. 15 (2014), No. 2, pp. 383-392