Biplanes with flag-transitive automorphism groups of almost simple type, with classical socle

摘要

In this paper we prove that if a biplane D admits a flag-transitive automorphism group G of almost simple type with classical socle, then D is either the unique (11,5,2) or the unique (7,4,2) biplane, and G≤PSL 2(11) or PSL 2(7), respectively. Here if X is the socle of G (that is, the product of all its minimal normal subgroups), then X?G≤Aut G and X is a simple classical group.