INVERSE ZERO-SUM PROBLEMS IN FINITE ABELIAN p-GROUPS

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.