Block-transitive $t$-($k^2,k,\lambda$) designs with $PSL(n,q)$ as socle

Guoqiang Xiong; Haiyan Guan

Block-transitive $t$-($k^2,k,\lambda$) designs with $PSL(n,q)$ as socle

Group Theory 2025-11-14 v1

Authors: Guoqiang Xiong , Haiyan Guan

Abstract

Let $\mathcal{D}=(\mathcal{P},\mathcal{B})$ be a non-trivial block-transitive $t$ - $(k^2,k,\lambda)$ 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 $2$ - $(144,12,\lambda)$ design with $\lambda\in\{3,6,12\}$ if $\lambda\mid k$ .

Keywords

flag-transitive designs

Cite

@article{arxiv.2511.10095,
  title  = {Block-transitive $t$-($k^2,k,\lambda$) designs with $PSL(n,q)$ as socle},
  author = {Guoqiang Xiong and Haiyan Guan},
  journal= {arXiv preprint arXiv:2511.10095},
  year   = {2025}
}

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