Inverse zero-sum problems

Abstract

Let G be an additive finite abelian group with exponent exp(G) = n. We define some central invariants in zero-sum theory: Let • D(G) denote the smallest integer l ∈ N such that every sequence S over G of length |S| ≥ l has a zero-sum subsequence. • η(G) denote the smallest integer l ∈ N such that every sequence S over G of length |S| ≥ l has a zero-sum subsequence T of length |T | ∈ [1, n]. • s(G) denote the smallest integer l ∈ N such that every sequence S over G of length |S| ≥ l has a zero-sum subsequence T of length |T | = n.