Almost simple groups as flag-transitive automorphism groups of symmetric designs with λ prime

Abstract

In this article, we study symmetric designs with λ prime admitting a flag-transitive and point-primitive automorphism groups G of almost simple type. We prove that either D is one of the six well-known examples of biplanes and triplanes, or D is the point- hyperplane design of PG(n−1,q) with λ = (q^{n−2}−1)/(q−1) prime and X = PSLn(q).