Automorphism groups of linear spaces and their parabolic subgroups (Q1003616)

The main result of the paper is the following theorem: If \(S\) is a finite linear space, \(G\) is an almost simple group acting on \(S\) simple transitively, the socle \(T\) of \(G\) is a simple group of Lie type, and the stabilizer \(G_x\) of a point \(x\in S\) intersects \(T\) in a parabolic subgroup, then \(G\) acts on \(S\) flag transitively.