Flag-transitive 2-designs with the prime square replication number

Abstract

In this note, we show that if G is a flag-transitive automorphism group of a symmetric 2-design D with the prime square replication number, then G is point-primitive of affine or almost simple type. If D is a non-symmetric 2-design and G is a primitive group, then G is of affine, almost simple or product type with G≤H≀S2 acting on P=Δ×Δ, where H is a primitive group on Δ.