Degree bound for separating invariants of abelian groups

Abstract

It is proved that the universal degree bound for separating polynomial invariants of a finite abelian group (in non-modular characteristic) is typically strictly smaller than the universal degree bound for generators of polynomial invariants. More precisely, these degree bounds can be equal only if the group is cyclic or is the direct sum of r r even order cyclic groups where the number of two-element direct summands is not less than the integer part of the half of r r . A characterization of separating sets of monomials is given in terms of zero-sum sequences over abelian groups.