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. (c) 2006 Elsevier Inc. All rights reserved.