On The Relations Between Subgroups of a Group and Submodules of Modules over Group Rings

Let R be a commutative ring and G a finite group. In [1], using a structure on an R module M to make it an RG module, we find some relations between RG submodules and a subgroups. We also prove that for each normal subgroup H of G with an invertible IHI in R, there is a direct summand RG submodule of M.