Flag-transitive point-quasiprimitive automorphism groups of 2-designs with lambda = 4

摘要

Let D be a non-trivial 2-(v, k, A) design with lambda = 4, and G = Aut(D) be flag-transitive, point-quasiprimitive, then G is of holomorph affine or almost simple type. As a corollary, we obtain that G cannot be an almost simple group if lambda = 3, and also obtain a classification of flag-transitive, point-quasiprimitive and imprimitive 2-(v, k, 4) designs. (C) 2018 Elsevier B.V. All rights reserved.