Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2412.03057 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912143646916608 |
|---|---|
| author | Gan, Yunsong Liu, Weijun Xia, Binzhou |
| author_facet | Gan, Yunsong Liu, Weijun Xia, Binzhou |
| contents | A regular bipartite graph $Γ$ is called semisymmetric if its full automorphism group $\mathrm{Aut}(Γ)$ acts transitively on the edge set but not on the vertex set. For a subgroup $G$ of $\mathrm{Aut}(Γ)$ that stabilizes the biparts of $Γ$, we say that $Γ$ is $G$-biprimitive if $G$ acts primitively on each part. In this paper, we first provide a method to construct infinite families of biprimitive semisymmetric graphs admitting almost simple groups. With the aid of this result, a classification of $G$-biprimitive semisymmetric graphs is obtained for $G=\mathrm{A}_n$ or $\mathrm{S}_n$. In pursuit of this goal, we determine all pairs of maximal subgroups of $\mathrm{A}_n$ or $\mathrm{S}_n$ with the same order and all pairs of almost simple groups of the same order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On biprimitive semisymmetric graphs Gan, Yunsong Liu, Weijun Xia, Binzhou Group Theory A regular bipartite graph $Γ$ is called semisymmetric if its full automorphism group $\mathrm{Aut}(Γ)$ acts transitively on the edge set but not on the vertex set. For a subgroup $G$ of $\mathrm{Aut}(Γ)$ that stabilizes the biparts of $Γ$, we say that $Γ$ is $G$-biprimitive if $G$ acts primitively on each part. In this paper, we first provide a method to construct infinite families of biprimitive semisymmetric graphs admitting almost simple groups. With the aid of this result, a classification of $G$-biprimitive semisymmetric graphs is obtained for $G=\mathrm{A}_n$ or $\mathrm{S}_n$. In pursuit of this goal, we determine all pairs of maximal subgroups of $\mathrm{A}_n$ or $\mathrm{S}_n$ with the same order and all pairs of almost simple groups of the same order. |
| title | On biprimitive semisymmetric graphs |
| topic | Group Theory |
| url | https://arxiv.org/abs/2412.03057 |