On integral representations

Let G be a finite group and p a prime.G is called cyclic mod p if there exists a normal ^-subgroup N^G such that G/N is cyclic.Let R be a commutative ring with lÇzR.Write (S#(G) for the set of subgroups USGj which are cyclic mod p for some appropriate prime p ( = p(U)) with pRj^R.An i£G-module M is a finitely generated i£-module, on which G acts from the left by i?-automorphisms.If U^G we write M for the R [/-module, one gets by restricting the action of G on the i?module M to U.