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 Word: symmetric design   flag-transitive   point-primitive   classical group  
Fund ProjectL: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).
Author NameAffiliation
Yan ZHU School of Basic Education Sciences, Xuzhou Medical University, Jiangsu 221004, P. R. China 
Shenglin ZHOU School of Mathematics, South China University of Technology, Guangdong 510640, P. R. China 
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      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 ${\rm Soc}(G)={\rm PSL}_2(9)$.
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