Zero-sum subsequences in abelian non-cyclic groups

Abstract

LetG be a finite abelian group,G∉{Zn, Z2⊺Z2n}. Then every sequenceA={g1,...,gt} of\(t = \frac{{4\left| G \right|}}{3} + 1\) elements fromG contains a subsequenceB⊂A, |G|=|G| such that\(\sum\nolimits_{g_i \in B^{g_i } } { = 0 (in G)} \). This bound, which is best possible, extends recent results of [1] and [22] concerning the celebrated theorem of Erdos-Ginzburg-Ziv [21].