Sequences not containing long zero-sum subsequences

Let G be a finite abelian group (written additively), and let D(G) denote the Davenport's constant of G, i.e. the smallest integer d such that every sequence of d elements (repetition allowed) in G contains a nonempty zero-sum subsequence. Let S be a sequence of elements in G with \S\ >= D(G). We say S is a normal sequence if S contains no zero-sum subsequence of length larger than \S\ - D(G) + 1. In this paper we obtain some results on the structure of normal sequences for arbitrary G. If G = C-n + C-n and n satisfies some well-investigated property, we determine all normal sequences. Applying these results, we obtain correspondingly some results on the structure of the sequence S in G of length \S\ = \G\ + D(G) - 2 and S contains no zero-sum subsequence of length \G\. (C) 2005 Elsevier Ltd. All rights reserved.