Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.17547 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908376286363648 |
|---|---|
| author | Lei, Chuhan Zhan, Xiaoqin |
| author_facet | Lei, Chuhan Zhan, Xiaoqin |
| contents | This paper investigates $2$-$(v,5,λ)$ designs $\mathcal{D}$ admitting a block-transitive automorphism group $G$. We first prove that if $G$ is point-imprimitive, then $v$ must be one of 16, 21, or 81. We further provide a complete classification of all such designs for $v=16$ and $v=21$. Secondly, we demonstrate that if $G$ is point-primitive, then it must be of affine type, almost simple type, or product type. Additionally, we present a classification of pairs $(\mathcal{D},G)$ where $G$ is of product type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Block-Transitive Automorphism Groups of $2$-$(v,5,λ)$ Designs Lei, Chuhan Zhan, Xiaoqin Group Theory This paper investigates $2$-$(v,5,λ)$ designs $\mathcal{D}$ admitting a block-transitive automorphism group $G$. We first prove that if $G$ is point-imprimitive, then $v$ must be one of 16, 21, or 81. We further provide a complete classification of all such designs for $v=16$ and $v=21$. Secondly, we demonstrate that if $G$ is point-primitive, then it must be of affine type, almost simple type, or product type. Additionally, we present a classification of pairs $(\mathcal{D},G)$ where $G$ is of product type. |
| title | Block-Transitive Automorphism Groups of $2$-$(v,5,λ)$ Designs |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.17547 |