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 kH[V] and kG[V]. As a corollary of our main result we get that if kG[V] is a polynomial algebra and kH[V] is factorial then kH[V] is a graded hypersurface algebra.