On the Erdős–Ginzburg–Ziv constant of finite abelian groups of high rank

Let G be a finite abelian group. The Erdős–Ginzburg–Ziv constant s(G) of G is defined as 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|=exp(G). If G has rank at most two, then the precise value of s(G) is known (for cyclic groups this is the theorem of Erdős–Ginzburg–Ziv). Only very little is known for groups of higher rank. In the present paper, we focus on groups of the form , with n,r∈N and n⩾2, and we tackle the study of s(G) with a new approach, combining the direct problem with the associated inverse problem.