Flag-transitive and almost simple orbits in finite projective planes

Abstract

Let Π be a projective plane of order n and let G be a collineation group of Π with a point-orbit O of length v. We investigate the triple (Π,O,G) when O has the structure of a non trivial 2-(v,k,1) design, G induces a flag-transitive and almost simple automorphism group on O and n≤∑(O)=b+v+r+k.