The separating Noether number for all finite abelian groups

The separating Noether number β sep ( G ) of a finite group G is the minimal positive integer d such that for every finite G -module V , there is a separating set consisting of invariant polynomials of degree at most d . In this paper we obtain the exact value of the separating Noether number for all finite abelian groups via methods from additive combinatorics.