On the Davenport constant and on the structure of extremal zero-sum free sequences

Abstract

Let G = Cn1 �···�Cnr with 1 < n1 | ··· |nr be a finite abelian group, d ∗ (G) = n1 +···+nr r, and let d(G) denote the maximal length of a zerosum free sequence over G. Then d(G) � d ∗ (G), and the standing conjecture is that equality holds for G = C r. We show that equality does not hold for C2 � C rn, where n � 3 is odd and r � 4. This gives new information on the structure of extremal zero-sum free sequences over C rn.