On Flag-Transitive, Point-Quasiprimitive Symmetric 2-(<i>v</i>,<i>k</i>,<i>λ</i>) Designs with <i>λ</i> Prime

Abstract

This paper contributes to the classification of flag-transitive symmetric 2-(v,k,λ) designs with λ prime. We investigate the structure of flag-transitive, point-quasiprimitive automorphism groups (G) of such 2-designs by applying the classification of quasiprimitive permutation groups. It is shown that the automorphism groups (G) have either an abelian socle or a non-abelian simple socle. Moreover, according to the classification of finite simple groups, we demonstrate that point-quasiprimitivity implies point-primitivity of G, except when the socle of G is PSLn(q).

Keywords

• 2-design
• automorphism group
• quasiprimitivity
• flag-transitivity