On CI-property of normal Cayley digraphs over abelian groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916638978211840 |
|---|---|
| author | Ryabov, Grigory |
| author_facet | Ryabov, Grigory |
| contents | A Cayley digraph $Γ$ over a finite group $G$ is said to be CI if for every Cayley digraph $Γ^\prime$ over $G$ isomorphic to $Γ$, there is an isomorphism from $Γ$ to $Γ^\prime$ which is at the same time an automorphism of $G$. In the present paper, we study a CI-property of normal Cayley digraphs over abelian groups, i.e. such Cayley digraphs $Γ$ that the group $G_r$ of all right translations of $G$ is normal in $Aut(Γ)$. At first, we reduce the case of an arbitrary abelian group to the case of an abelian $p$-group. Further, we obtain several results on CI-property of normal Cayley digraphs over abelian $p$-groups. In particular, we prove that every normal Cayley digraph over an abelian $p$-group of order at most $p^5$, where $p$ is an odd prime, is CI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On CI-property of normal Cayley digraphs over abelian groups Ryabov, Grigory Combinatorics Group Theory 05C25, 05C60, 20B25 A Cayley digraph $Γ$ over a finite group $G$ is said to be CI if for every Cayley digraph $Γ^\prime$ over $G$ isomorphic to $Γ$, there is an isomorphism from $Γ$ to $Γ^\prime$ which is at the same time an automorphism of $G$. In the present paper, we study a CI-property of normal Cayley digraphs over abelian groups, i.e. such Cayley digraphs $Γ$ that the group $G_r$ of all right translations of $G$ is normal in $Aut(Γ)$. At first, we reduce the case of an arbitrary abelian group to the case of an abelian $p$-group. Further, we obtain several results on CI-property of normal Cayley digraphs over abelian $p$-groups. In particular, we prove that every normal Cayley digraph over an abelian $p$-group of order at most $p^5$, where $p$ is an odd prime, is CI. |
| title | On CI-property of normal Cayley digraphs over abelian groups |
| topic | Combinatorics Group Theory 05C25, 05C60, 20B25 |
| url | https://arxiv.org/abs/2503.00859 |