On a zero-sum problem arising from factorization theory

TL;DR

This paper investigates a zero-sum problem related to minimal zero-sum sequences in finite abelian groups, providing insights into the structure of sets of lengths with maximal elasticity in transfer Krull monoids.

Contribution

It offers a structural description of sets of lengths with maximal elasticity based on solving a zero-sum problem in factorization theory.

Findings

Structural description of sets of lengths with maximal elasticity

Solution to a zero-sum problem in finite abelian groups

Insights into transfer Krull monoids

Abstract

We study a zero-sum problem dealing with minimal zero-sum sequences of maximal length over finite abelian groups. A positive answer to this problem yields a structural description of sets of lengths with maximal elasticity in transfer Krull monoids over finite abelian groups.