A NOTE ON FLAG-TRANSITIVE 5-(v, k, 4) DESIGNS

Abstract

This article is a contribution to the study of the automorphism groups of $5$-$(v,k,4)$ designs. Let ${\mathcal S}$=$({\mathcal P},{\mathcal B})$ be a non-trivial $5$-$(q+1,k,4)$ design. If $G$ acts flag-transitively on $\mathcal S$, then $G$ is not two-dimensional projective linear group $PSL(2,q)$.