Flag-transitive point-primitive $(v,k,4)$ symmetric designs with exceptional socle of Lie type

Abstract

Let $G$ be an automorphism group of a‎ ‎$2$-$(v,k,4)$ symmetric design $mathcal D$‎. ‎In this paper‎, ‎we‎ ‎prove that if $G$ is flag-transitive point-primitive‎, ‎then the‎ ‎socle of $G$ cannot be an exceptional group of Lie type‎.