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Peer-reviewedCC BY 4.0Algebraic Combinatorics

Dihedral groups of square-free order are DCI-groups

  • István Kovács1
  • Gábor Somlai2
  1. 1University of Primorska, UP IAM and UP FAMNIT, Muzejski trg 2 and Glagoljaška 8, SI-6000 Koper (Slovenia)
  2. 2Eötvös Loránd University, Department of Algebra and Number Theory, Pázmány Péter sétány 1/C, H-1117 Budapest (Hungary)
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Abstract

A finite group G is called a DCI-group if any two isomorphic Cayley digraphs of G are also isomorphic via an automorphism of G . If G is a non-abelian generalised dihedral DCI-group, then Dobson, Muzychuk, and Spiga proved that G 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.

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Cite

BibTeXRIS
BibTeX
@article{kovacs2026dihedral,
  title = {{Dihedral groups of square-free order are DCI-groups}},
  author = {István Kovács and Gábor Somlai},
  journal = {Algebraic Combinatorics},
  year = {2026},
  month = oct,
  doi = {10.5802/alco.514},
  url = {https://alco.centre-mersenne.org/articles/10.5802/alco.514/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Dihedral groups of square-free order are DCI-groups
AU  - István Kovács
AU  - Gábor Somlai
PY  - 2026
DA  - 2026/10/27
JO  - Algebraic Combinatorics
DO  - 10.5802/alco.514
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.514/
AB  - A finite group G is called a DCI-group if any two isomorphic Cayley digraphs of G are also isomorphic via an automorphism of G . If G is a non-abelian generalised dihedral DCI-group, then Dobson, Muzychuk, and Spiga proved that G 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.
SN  - 2589-5486
ER  -