International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 327-338
On rank projective planes
Département de mathématiques, Ecole polytechnique fédérale, Lausanne CH-1015, Swaziland
Received 29 December 1983; Revised 16 April 1984
Copyright © 1984 Otto Bachmann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we continue the study of projective planes which admit collineation groups of low rank (Kallaher  and Bachmann [2,3]). A rank collineation group of a projective plane of order is proved to be flag-transitive. As in the rank and rank case this implies that is not desarguesian and that is (a prime power) of the form if is odd and with if is even. Our proof relies on the classification of all doubly transitive groups of finite degree (which follows from the classification of all finite simple groups).