On a theorem of gobel on permutation invariants

Abstract

Let F be a field, let S = F[X1,..., Xn] be a polynomial ring on variables X1,..., Xn, and let G be a group of permutations of {X1,..., Xn}. Gobel proved that for n ≥ 3 the ring of invariants SG is generated by homogeneous elements of degree at most [image omitted]. In this article, we obtain reductions in the set of generators introduced by Gobel and sharpen his bound for almost all permutation groups over any ground field. Copyright © Taylor & Francis Group, LLC.