Flag-transitive $4$-$(v,k,5)$ designs and $PSL(2,q)$ groups

Huili Dong

Published 2019-08-02Version 1

This paper is a contribution to the classification of flag-transitive $4$-$(v,k,\lambda)$ designs. Let $\cal D$ be a nontrivial $4$-$(q+1,k,5)$ design with the automorphism simple group $G=PSL(2,q)$ acting flag-transitively. Then up to isomorphism $\cal D$ is a unique $4$-$(9,8,5)$ design with $G_B={E_8}\rtimes {C_7}$ or a unique $4$-$(24,8,5)$ design with $G_B=D_8$.