On Short Zero-Sum Subsequences II

Abstract

Let G be a finite abelian group of exponent n. In this paper we investigate the structure of the maximal (in length) sequences over G that contain no zero-sum subsequence of length [at most] n. Among others, we obtain a result on the multiplicities of elements in these sequences, which support well-known conjectures on the structure of these sequences. Moreover, we investigate the related invariants s(G) and η(G), which are defined as the smallest integer l such that every sequence over G of length at least l has a zero-sum subsequence of length n (at most n, respectively). In particular, we obtain the precise value of s(G) for certain groups of rank 3.