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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2509.02778 |
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| _version_ | 1866909768066531328 |
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| author | Kovács, István Somlai, Gábor |
| author_facet | Kovács, István Somlai, Gábor |
| contents | A finite group $G$ is a 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dihedral groups of square-free order are DCI-groups Kovács, István Somlai, Gábor Group Theory 05E18, 05E30 A finite group $G$ is a 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. |
| title | Dihedral groups of square-free order are DCI-groups |
| topic | Group Theory 05E18, 05E30 |
| url | https://arxiv.org/abs/2509.02778 |