On Zero-Sum Subsequences of Restricted Size

Abstract

LetGbe a finite abelian group with exponente, letr(G) be the minimal integertwith the property that any sequence oftelements inGcontains ane-term subsequence with sum zero. In this paper we show that ifr(C2n)=4n−3 and ifn⩾((3m−4)(m−1)m2+3)/4m, thenr(C2nm)=4nm−3. In particular, this result implies thatr(C2nm1…mr)=4nm1…mr−3 provided thatn=2a3b5c7d,m1⩾…⩾mrandn⩾((3m1−4)(m1−1)m21+3)/4m1.