Inductive Methods and Zero-sum Free Sequences
نویسندگان
چکیده
A fairly long-standing conjecture is that the Davenport constant of a group G = Zn1 ⊕ · · · ⊕ Znk with n1| . . . |nk is 1 + ∑k i=1(ni − 1). This conjecture is false in general, but it remains to know for which groups it is true. By using inductive methods we prove that for two fixed integers k and ! it is possible to decide whether the conjecture is satisfied for all groups of the form Zk ⊕ Zn with n co-prime to k. We also prove the conjecture for groups of the form Z3 ⊕ Z3n ⊕ Z3n, where n is co-prime to 6, assuming a conjecture about the maximal zero-sum free sets in Zn. Received: 4/23/08, Revised: 5/22/09, Accepted: 5/25/09, Published: 10/1/09
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