| Flag-Transitive Point-Primitive $(v,k,4)$-Symmetric Designs with ${\rm PSL}_n(q)$ as Socle |
| Received:March 28, 2017 Revised:September 15, 2017 |
| Key Words:
symmetric design flag-transitive point-primitive classical group
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11471123; 11626206) and the Scientific Research Foundation for Excellent Talents of Xuzhou Medical University (Grant No.D2016002). |
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| Abstract: |
| Let $\cal D$ be a nontrivial symmetric $(v,k,4)$ design, and $G\leq {\rm Aut}(\cal D)$ be flag-transitive and point-primitive with ${\rm PSL}_n(q)$ as socle. Then $\cal D$ is a $2$-$(15,8,4)$ symmetric design and ${\rm Soc}(G)={\rm PSL}_2(9)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.01.003 |
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