Subgroups of a finite group whose algebra of invariants is a complete intersection

Abstract

Let G be a finite subgroup of GL(V), where V is a finite-dimensional vector space over the field K and char K∤∣G∣. We show that if the algebra of invariants K(V)^G of the symmetric algebra of V is a complete intersection then K(V)^H is also a complete intersection for all subgroups H of G such that H={σ ε Gv σ(v)=v for all v ε V^H}.