On modules over group rings of soluble groups with commutative ring of scalars

The author studies an $\mathbf RG$-module $A$ such that $\mathbf R$ is a commutative ring, $A/C_{A}(G)$ is not a Noetherian $\mathbf R$-module, $C_{G}(A)=1$, $G$ is a soluble group. The system of all subgroups $H\leq G$, for which the quotient modules $A/C_{A}(H)$ are not Noetherian $\mathbf R$-modules, satisfies the maximal condition. This condition is called the condition max–nnd. The structure of the group $G$ is described.