Summary: 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 \(\text{s}(G)\) and \(\eta(G)\), 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 \(\text{s}(G)\) for certain groups of rank \(3\).
Part I, see Ars Comb. 74, 231–238 (2004; Zbl 1201.11031).