On A Property Of Minimal Zero-Sum Sequences And Restricted Sumsets

Let G be an additively written abelian group, and let S be asequence in G \ {0} with length |S| 4. Suppose that S is aproduct of two subsequences, say S = BC, such that the elementg + h occurs in the sequence S whenever g.h is a subsequenceof B or of C. Then S contains a proper zero-sum subsequence,apart from some well-characterized exceptional cases. This resultis closely connected with restricted set addition in abeliangroups. Moreover, it solves a problem on the structure of minimalzero-sum sequences, which recently occurred in the theory ofnon-unique factorizations. 2000 Mathematics Subject Classification11B50, 11B75, 11P99.