| Classification of Flag-Transitive Primitive Symmetric $(v,k,\lambda)$ Designs with $PSL(2,q)$ as Socle |
| Revised:September 14, 2015 |
| Key Words:
symmetric design flag-transitive primitive group
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.\,11471123; 11426066) and the Natural Science Foundation of Guangdong Province (Grant No.\,S2013010011928). |
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| Abstract: |
| $\cal D$ 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 $(15, 8, 4)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.02.001 |
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