  We consider the class $\mathfrak M$ of $\bf R$--modules where $\bf R$ is an
associative ring. Let $A$ be a module over a group ring $\bf R$$G$ where $G$ is
a group and let $\mathfrak L(G)$ be a set of all proper subgroups of $G$ such
that if $H \in \mathfrak L(G)$ then $A/C_{A}(H)$ belongs to $\mathfrak M$. We
study an $\bf R$$G$--module $A$ such that $G \not = G'$, $C_{G}(A) = 1$,
$A/C_{A}(G) \not \in \mathfrak M$, and $\mathfrak M$ is one of the classes:
artinian $\bf R$--modules, minimax $\bf R$--modules, finite $\bf R$--modules.
We consider the cases: 1) $\mathfrak M$ is a class of all artinian $\bf
R$--modules, $\bf R$ is either a ring of integers or a ring of $p$--adic
integers; 2) $\mathfrak M$ is a class of all minimax $\bf R$--modules, $\bf R$
is a ring of integers, G is a locally soluble group; 3) $\mathfrak M$ is a
class of all finite $\bf R$--modules, $\bf R$ is an associative ring. In these
cases we prove that $G$ is isomorphic to a quasi--cyclic $q$--group for some
prime $q$.
