On a Permutation Problem for Finite Abelian Groups

[摘要] Let $G$ be a finite additive abelian group with exponent $n>1$, and let $a_1,\ldots,a_{n-1}$ be elements of $G$. We show that there is a permutation $\sigma\in S_{n-1}$ such that all the elements $sa_{\sigma(s)}\ (s=1,\ldots,n-1)$ are nonzero if and on

[学科分类] 离散数学和组合数学

[关键词] Combinatorial number theory;Abelian group;Permutation;Subset sum