On modules over group rings of groups with restrictions on the system of all proper subgroups

We consider the class $\mathfrak{M}$ of $\mathbf{R}$–modules where $\mathbf{R}$ is an associative ring. Let $A$ be a module over a group ring $\mathbf{R}$$G$ where $G$ is a group and let $\mathfrak{L}(G)$ be a set of all proper subgroups of $G$ such that if $H\in \mathfrak{L}(G)$ then $A\mathrm{/}{C}_A(H)$ belongs to $\mathfrak{M}$. We study an $\mathbf{R}$$G$–module $A$ such that $G≠G^{\mathrm{\prime }}$, $C_G(A)=1$, $A\mathrm{/}{C}_A(G)\in ̸\mathfrak{M}$, and $\mathfrak{M}$ is one of the classes: artinian $\mathbf{R}$–modules, minimax $\mathbf{R}$–modules, finite $\mathbf{R}$–modules. We consider the cases: 1) $\mathfrak{M}$ is a class of all artinian $\bf R$--modules,$\bf R$iseitheraringofintegersoraringof$p$–adic integers; 2) $\mathfrak{M}$ is a class of all minimax $\mathbf{R}$–modules, $\mathbf{R}$ is a ring of integers, G is a locally soluble group; 3) $\mathfrak{M}$ is a class of all finite $\mathbf{R}$–modules, $\mathbf{R}$ is an associative ring. In these cases we prove that $G$ is isomorphic to a quasi–cyclic $q$–group for some prime $q$.