On flag-transitive automorphism groups of symmetric designs

Abstract

In this article, we study flag-transitive automorphism groups of non-trivial symmetric (v, k, λ) designs, where λ divides k and k ≥ λ². We show that such an automorphism group is either point-primitive of affine or almost simple type, or point-imprimitive with parameters v = λ²(λ + 2) and k = λ(λ + 1), for some positive integer λ. We also provide some examples in both possibilities.