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Abstract

We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian $p$-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian $p$-groups. Among other consequences, our method implies that, if we denote by $\exp(G)$ the exponent of the finite Abelian $p$-group $G$ considered, every zero-sumfree sequence $S$ with maximal possible length over $G$ contains at least $\exp(G)-1$ elements of order $\exp(G)$, which improves a previous result of W. Gao and A. Geroldinger.