Hypersurfaces in modular invariant theory

Let the finite group G act linearly on the n-dimensional vector space V over the field k of characteristic p 0. Suppose H G is a normal subgroup of index ℓ, a prime number. In this paper we shall study the relationship between the two invariant rings k[V]H and k[V]G. As a corollary of our main result we get that if k[V]G is a polynomial algebra and k[V]H is factorial then k[V]H is a graded hypersurface algebra.