Homogeneity of induced modules (Q1825268)

Let N be a normal subgroup of a finite group G, let R be a commutative ring which is either artinian or a complete noetherian local ring, and let R/J(R) be of prime characteristic p. We prove that if V is a finitely generated indecomposable RN-module such that H/N is a p-group, where H is the inertia group of V, then \(V^ G\cong eU\) for some positive integer e and some indecomposable RG-module U.