Zero-sum subsequences of distinct lengths

Abstract

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 [Formula: see text], 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).