Unsolvable Block-Transitive Automorphism Groups of \(2 – (v, 31,1)\) Designs

Abstract

This paper contributes to the study of automorphism groups of \(2-(v, k, 1)\) designs. Let \(\mathcal{D}\) be a \(2-(v, 31, 1)\) design and \(G \leq Aut(\mathcal{D})\) be block-transitive and point-primitive. If \(G\) is unsolvable, then \(Soc(G)\), the socle of \(G\), is not isomorphic to \(^2F_4(q)\).