Block transitive \(2 – (v, 13,1)\) Designs and Suzuki Groups

Abstract

This article is a contribution to the study of the automorphism groups of \(2\)-\((v,k,1)\) designs. Let \(\mathcal{D}\) be a \(2\)-\((v,13,1)\) design, \(G \leq \mathrm{Aut}(\mathcal{D})\) be block transitive and point primitive. If \(G\) is unsolvable, then \(\mathrm{Soc}(G)\), the socle of \(G\), is not \(\mathrm{Sz}(q)\).