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

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 the six well-known examples biplanes triplanes, or point- hyperplane design PG(n−1,q) = (q^{n−2}−1)/(q−1) X PSLn(q).