International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 2, Pages 305-319
doi:10.1155/S0161171281000185
On rank 4 projective planes
Département de mathématiques, Ecole polytechnique fédérale, Lausanne CH-1007, Swaziland
Received 4 October 1979
Copyright © 1981 O. 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.
Abstract
Let a finite projective plane be called rank m plane if it admits a collineation group G of rank m, let it be called strong rank m plane if moreover GP=G1 for some point-line pair (P,1). It is well known that every rank 2 plane is desarguesian (Theorem of Ostrom and Wagner). It is conjectured that the only rank 3 plane is the plane of order 2. By [1] and [7] the only strong rank 3
plane is the plane of order 2. In this paper it is proved that no strong rank 4 plane exists.