Zero-sum invariants of finite abelian groups

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 $\mathrm{\Omega }\subset B(G$), let $d_{\mathrm{\Omega }}(G)$ be the smallest integer $t$ such that every sequence $S$ over $G$ of length $\mathrm{\mid }S\mathrm{\mid }\ge t$ has a subsequence in $\mathrm{\Omega }$.We provide some first results and open problems on $d_{\mathrm{\Omega }}(G)$.