On a class of modules over group rings of soluble groups with restrictions on some systems of subgroups

The author studies a $\mathbf DG$-module $A$ such that $\mathbf D$ is a Dedekind domain, $A/C_A(G)$ is not an Artinian $\mathbf D$-module, $C_A(G)=1$, $G$ is a soluble group, and the system of all subgroups $H\leq G$ for which the quotient modules $A/C_A(H)$ are not Artinian $\mathbf D$-modules satisfies the minimum condition. The structure of $G$ is described.