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A fairly long-standing conjecture is that the Davenport constant of a group  G  = ℤ  n  1   ⊕ ⋯ ⊕ ℤ  n k    with  n  1  | ⋯ |  n k   is   . 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    with  n  co-prime to  k .

Inductive Methods and Zero-Sum Free Sequences