Block-transitive $t$-($k^2,k,λ$) designs with $PSL(n,q)$ as socle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912706549776384 |
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| author | Xiong, Guoqiang Guan, Haiyan |
| author_facet | Xiong, Guoqiang Guan, Haiyan |
| contents | Let $\mathcal{D}=(\mathcal{P},\mathcal{B})$ be a non-trivial block-transitive $t$-$(k^2,k,λ)$ design with $G\leq \Aut(\mathcal{D})$ and $X\unlhd G\leq \Aut(X)$, where $X=PSL(n,q)(n\geq3).$ We prove that $t=2$ and the parameters $(n,q,v,k)$ is $(3,3,144,12),(4,7,400,20)$ or $(5,3,121,11).$ Moreover, $\mathcal{D}$ is a $2$-$(144,12,λ)$ design with $λ\in\{3,6,12\}$ if $λ\mid k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Block-transitive $t$-($k^2,k,λ$) designs with $PSL(n,q)$ as socle Xiong, Guoqiang Guan, Haiyan Group Theory Let $\mathcal{D}=(\mathcal{P},\mathcal{B})$ be a non-trivial block-transitive $t$-$(k^2,k,λ)$ design with $G\leq \Aut(\mathcal{D})$ and $X\unlhd G\leq \Aut(X)$, where $X=PSL(n,q)(n\geq3).$ We prove that $t=2$ and the parameters $(n,q,v,k)$ is $(3,3,144,12),(4,7,400,20)$ or $(5,3,121,11).$ Moreover, $\mathcal{D}$ is a $2$-$(144,12,λ)$ design with $λ\in\{3,6,12\}$ if $λ\mid k$. |
| title | Block-transitive $t$-($k^2,k,λ$) designs with $PSL(n,q)$ as socle |
| topic | Group Theory |
| url | https://arxiv.org/abs/2511.10095 |