On the Erdős–Ginzburg–Ziv constant of groups of the form C2r ⊕ Cn

Abstract

Let [Formula: see text] be a finite abelian group. The Erdős–Ginzburg–Ziv constant [Formula: see text] of [Formula: see text] is defined as the smallest integer [Formula: see text] such that every sequence [Formula: see text] over [Formula: see text] of length [Formula: see text] has a zero-sum subsequence [Formula: see text] of length [Formula: see text]. The value of this classical invariant for groups with rank at most two is known. But the precise value of [Formula: see text] for the groups of rank larger than two is difficult to determine. In this paper, we pay attention to the groups of the form [Formula: see text], where [Formula: see text] and [Formula: see text]. We give a new upper bound of [Formula: see text] for odd integer [Formula: see text]. For [Formula: see text], we obtain that [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text].