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Zero-sum subsequences of distinct lengths

Let G be an additive finite abelian group, and let disc(G) denote the smallest positive integer t such that every sequence S over G of length ∣S∣ ≥ t has two nonempty zero-sum subsequences of distinct lengths. We determine disc(G) for some groups including the groups , the groups of rank at most two and the groups Cmpn ⊕ H, where m, n are positive integers, p is a prime and H is a p-group with pn ≥ D*(H).