Gregor Kemper
Universitaet Heidelberg

"Lower Degree Bounds for Modular Invariants and a Question of I. Hughes",
IWR-Preprint 97-40, Heidelberg 1997

Abstract:

We prove two statements. The first one is a conjecture of Ian Hughes
which states that if f_1,...,f_n are primary invariants of a finite
linear group G, then the least common multiple of the degrees of the
f_i is a multiple of the exponent of G.

The second statement is about vector invariants: If G is a
permutation group and K a field of positive characteristic p such
that p divides |G|, then the invariant ring K[V^m]^G of m
copies of the permutation module V over K requires a generator of
degree m*(p-1). This improves a bound given by Richman, and
implies that there exists no degree bound for the invariants of G
which is independent of the representation.