On zero-sum subsequences in a finite abelian p-group of length not exceeding a given number

Let G be a finite abelian group. For any integer a≥1, we define the constant s≤a(G) as the least positive integer t such that any sequence S over G of length at least t has a zero-sum subsequence of length ≤a in it. In this article, we compute this constant for many classes of abelian p-groups. In particular, it proves a conjecture of Schmid and Zhuang [20].