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

Let D be a nontrivial symmetric(v, k, λ) design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on 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).