On the Davenport constant and on the structure of extremal zero-sum free sequences (Q452839)

The authors consider the maximal length, \(d(G)\); of a zero-sum free sequence over a finite abelian group \(G\). Let \(G = C_{n_1}\oplus\dots\oplus C_{n_r}\), and set \(D^*(G) = n_1 + \dots + n_r - r\). They provide a proof that the long-standing conjecture of equality \(d(G) = d^*(G)\) does not hold when \(n \geq 3\) is odd and \(r\geq 4\). They also provide new information on the structure of extremal zero-sum sequences over \(C^r_{2n}\).