On the generalized Davenport constant and the Noether number

TL;DR

This paper extends known results from zero-sum sequence theory to polynomial invariants of finite groups, providing improved bounds on degrees of invariants that vanish at the zero vector.

Contribution

It introduces a generalized Noether number framework for arbitrary finite groups and establishes sharper upper bounds on invariant degrees.

Findings

Extended Davenport constant results to Noether numbers for finite groups

Provided improved upper bounds on degrees of polynomial invariants

Applicable to non-cyclic finite groups

Abstract

Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.