On zero-sum subsequences of length not exceeding a given number.

Let G be an additive finite abelian group. For a positive integer k , let s ≤ k ( G ) denote the smallest integer l such that each sequence of length l has a non-empty zero-sum subsequence of length at most k . Among other results, we determine s ≤ k ( G ) for all finite abelian groups of rank two. [ABSTRACT FROM AUTHOR]