Transitive projective planes and 2-rank

Abstract

Suppose that a group $G$ acts transitively on the points of a non-Desarguesian plane, $\mathcal{P}$. We prove first that the Sylow 2-subgroups of $G$ are cyclic or generalized quaternion. We also prove that $\mathcal{P}$ must admit an odd order automorphism group which acts transitively on the set of points of $\mathcal{P}$.

29 pages. This version is significantly expanded (9 extra pages). Proofs which were formerly omitted or only sketched are now given in detail. In addition the exposition is (hopefully) much more readable