International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 12, Pages 757-762
On some hyperbolic planes from finite projective planes
Department of Mathematics, Faculty of Sciences and Art, Uludag University, Bursa, Görükle 16059, Turkey
Received 5 October 1999; Revised 15 November 2000
Copyright © 2001 Basri Celik. 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.
Let be a finite projective plane of order , and let be a subplane of with
order which is not a Baer subplane (i.e., ). Consider the substructure with , where stands for the restriction of to . It is shown that every is a hyperbolic plane, in
the sense of Graves, if . Also we give some combinatorial properties of the line
classes in hyperbolic planes, and some
relations between its points and lines.