Permutations over cyclic groups

Abstract

Generalizing a result in the theory of finite fields we prove that, apart from a couple of exceptions that can be classified, for any elements $a_1,...,a_m$ of the cyclic group of order $m$, there is a permutation $\pi$ such that $1a_{\pi (1)}+...+m{a}_{\pi (m)}=0$.

References in corpus (1)

• On types and classes of commuting matrices over finite fields

Cited by in corpus (1)

• Distinct coordinate solutions of linear equations over finite fields