Subsequence sums of zero-sum free sequences over finite abelian groups
Volume 140 / 2015
Colloquium Mathematicum 140 (2015), 119-127
MSC: Primary 11B50; Secondary 11P99.
DOI: 10.4064/cm140-1-10
Abstract
Let $G$ be a finite abelian group of rank $r$ and let $X$ be a zero-sum free sequence over $G$ whose support $\mathrm {supp}(X)$ generates $G$. In 2009, Pixton proved that $|\varSigma (X)|\geq 2^{r-1}(|X|-r+2)-1$ for $r \le 3$. We show that this result also holds for abelian groups $G$ of rank $4$ if the smallest prime $p$ dividing $|G|$ satisfies $p\geq 13$.
