Classification of flag-transitive primitive symmetric $(v,k,\lambda )$ designs with $PSL(2,q)$ as socle

Abstract

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

17 pages, 3 tables