ON MODULES OVER GROUP RINGS OF GROUPS WITH RESTRICTIONS ON THE SYSTEM OF ALL PROPER SUBGROUPS

Abstract

We consider the class M of R–modules where R is an associative ring. Let A be a module over a group ring RG, G be a group and let L(G) be the set of all proper subgroups of G. We suppose that if H ∈ L(G) then A/CA(H) belongs to M. We investigate an RG–module A such that G = G′, CG(A) = 1. We study the cases: 1) M is the class of all artinian R–modules, R is either the ring of integers or the ring of p–adic integers; 2) M is the class of all finite R–modules, R is an associative ring; 3) M is the class of all finite R–modules, R= F is a finite field.