Flag-transitive Point-primitive symmetric designs and three dimensional projective special linear groups

‎The main aim of this article is to study $(v,k,\lambda)$-symmetric designs admitting a flag-transitive and point-primitive automorphism group $G$ whose socle is $\PSL(3‎, ‎q)$‎. ‎We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane $\PG(2,q)$ and $G\geq \PSL(3‎, ‎q)$.