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October 13, 2025Open Access

On the separating Noether number of finite abelian groups

Key Points

The study determines the exact values of the separating Noether number for certain finite abelian groups.
Key results are obtained for groups that are either p-groups or possess ranks of 2, 3, or 5.
Methods from additive combinatorics are applied to investigate the relationship between group structures and polynomial invariants.
The paper emphasizes the role of invariant polynomials in determining the minimal integer defining the separating Noether number.

Abstract

The separating Noether number ₒ₄₏ (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 use methods from additive combinatorics to investigate the separating Noether number for finite abelian groups. Among others, we obtain the exact value of ₒ₄₏ (G), provided that G is either a p-group or has rank 2, 3 or 5.

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