A classification of flag-transitive block designs

摘要

In this article, we investigate 2-(v, k, lambda) designs with gcd(r, lambda) = 1 admitting flag-transitive automorphism groups G. We prove that if G is an almost simple group, then such a design belongs to one of the eight infinite families of 2-designs or it is one of the eleven well-known examples. We describe all these examples of designs. We, in particular, prove that if D is a symmetric (v, k, lambda) design with gcd(k, lambda) = 1 admitting a flag-transitive automorphism group G, then either G <= A Gamma L-1(q) for some odd prime power q, or D is the point-hyperplane design or the unique Hadamard design with parameters (11, 5, 2).