On flag-transitive automorphism groups of symmetric designs

Abstract

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