Permutations with a distinct divisor property

Mohammad Javaheri; Nikolai A. Krylov

paper

Permutations with a distinct divisor property

arXiv:1904.04227

Abstract

A finite group of order $n$ is said to have the distinct divisor property (DDP) if there exists a permutation $g_{1}, \dots, g_{n}$ of its elements such that $g_{i}^{- 1} g_{i + 1} \neq = g_{j}^{- 1} g_{j + 1}$ for all $1 \leq i < j < n$ . We show that an abelian group is DDP if and only if it has a unique element of order 2. We also describe a construction of DDP groups via group extensions by abelian groups and show that there exist infinitely many non abelian DDP groups.