PERMUTATIONS WITH A DISTINCT DIVISOR PROPERTY

Year 2021, Volume: 29 Issue: 29, 1 - 14, 05.01.2021

Mohammad Javaherı Nikolai A. Krylov

https://doi.org/10.24330/ieja.851969

Cited By: 1

Abstract

A finite group of order $n$ is said to have the distinct divisor pro-perty (DDP) if there exists a permutation $g_1,\ldots, g_n$ 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.

Keywords

Distinct difference property, distinct divisor property, central extension, semidirect product

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