Flag-transitive non-symmetric 2-designs with $ \lambda $ prime and exceptional groups of Lie type

Abstract

<p>This paper contributes to the classification of flag-transitive 2-$ (v, k, \lambda) $ designs. Let $ \mathcal{D} $ be a non-trivial and non-symmetric $ 2 $-$ (v, k, \lambda) $ design with $ \lambda $ prime and $ G $ be a flag-transitive point-primitive automorphism group of $ \mathcal{D} $. A recent work by the first author and Chen has proven that the socle of $G$ is either a nonabelian simple group or an elementary abelian $ p $-group for some prime $ p $. In this paper, we focus on the case where the socle of $G$ is an exceptional group of Lie type and give all possible parameters of such 2-designs.</p>