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

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 RG, G be a group and let \mathfrak L(G) be the set of all proper subgroups of G. We suppose that if H \in \mathfrak L(G) then A/C_{A}(H) belongs to \mathfrak M. We investigate an \bf RG--module A such that G \not = G', C_{G}(A) = ۱. We study the cases: ۱) \mathfrak M is the class of all artinian \bf R--modules, \bf R is either the ring of integers or the ring of p--adic integers; ۲) \mathfrak M is the class of all finite \bf R--modules, \bf R is an associative ring; ۳) \mathfrak M is the class of all finite \bf R--modules, \bf R=F is a finite field.

Keywords:

group ring , linear group , module