Dihedral groups of square-free order are DCI-groups
Group Theory
2025-09-04 v1
Abstract
A finite group is a called a DCI-group if any two isomorphic Cayley digraphs of are also isomorphic via an automorphism of . If is a non-abelian generalised dihedral DCI-group, then Dobson, Muzychuk, and Spiga proved that must be a dihedral group of square-free order (Ars Math. Contemp., 2022). In this paper, we prove that the converse statement also holds, i.\,e., all dihedral groups of square-free order are DCI-groups.
Cite
@article{arxiv.2509.02778,
title = {Dihedral groups of square-free order are DCI-groups},
author = {István Kovács and Gábor Somlai},
journal= {arXiv preprint arXiv:2509.02778},
year = {2025}
}