# Zero-sum invariants of finite abelian groups

## TL;DR

This paper introduces a unified framework for zero-sum invariants in finite abelian groups, defining key parameters and presenting initial results and open problems in the area.

## Contribution

It formulates a general approach to zero-sum invariants and provides initial findings and open questions for the invariant $d_{ ext{Omega}}(G)$.

## Key findings

- Initial results on the invariant $d_{ ext{Omega}}(G)$
- Open problems proposed for future research
- Framework unifying various zero-sum invariants

## Abstract

The purpose of the article is to provide an unified way to formulate zero-sum invariants. Let $G$ be a finite additive abelian group. Let $B(G)$ denote the set consisting of all nonempty zero-sum sequences over G. For $\Omega \subset B(G$), let $d_{\Omega}(G)$ be the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\geq t$ has a subsequence in $\Omega$.We provide some first results and open problems on $d_{\Omega}(G)$.