Projective planes with a transitive automorphism group (Q2501705)

This paper contains two theorems on finite projective planes: (1) Let \(G\) act line-transitively on a finite projective plane and let \(M\) be a minimal normal subgroup of \(G\). Then \(M\) is either abelian or simple or the order of the plane is 3, 9, 16 or 25; (2) Let \(G\) be a classical simple group which acts line-transitively on a finite projective plane. Then the rank of \(G\) is bounded.