以PSL(2,q)作为本原自同构群的旗传递对称$(v,k,\lambda)$设计的分类

Classification of Flag-Transitive Primitive Symmetric $(v,k,\lambda)$ Designs with $PSL(2,q)$ as Socle

中文关键词:  对称设计  旗传递  本原群

英文关键词:symmetric design  flag-transitive  primitive group

中文摘要:

      设$D$是一个非平凡的对称$(v,k,\lambda)$设计, $G$是$D$的一个自同构群.本文证明了如果$G$以二维典型群PSL$(2,q)$作为基柱且在$D$上的作用是旗传递和点本原的,那么设计$D$的参数只能为$(7, 3, 1)$, $(7, 4, 2)$, $(11, 5, 2)$, $(11, 6, 3)$或$(15, 8, 4)$.

英文摘要:

      $\cal D$ be a nontrivial symmetric $(v,k,\lambda)$ design, and $G$ be a subgroup of the full automorphism group of $\cal D$. In this paper we prove that if $G$ acts flag-transitively, point-primitively on $\mathcal{D}$ and ${\rm Soc}(G)={\rm PSL}(2,q)$, then $\mathcal{D}$ has parameters $(7, 3, 1)$, $(7, 4, 2)$, $(11, 5, 2)$, $(11, 6, 3)$ or $(15, 8, 4)$.