International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 605-608

A characterization of the desarguesian planes of order q2 by SL(2,q)

D. A. Foulser,1 N. L. Johnson,2 and T. G. Ostrom3

1Mathematics Department, University of Illinois at Chicago Circle, Chicago 60680, Illinois, USA
2Department of Mathematics, The University of Iowa, lowa City 52242, Iowa, USA
3Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USA

Received 25 January 1982

Copyright © 1983 D. A. Foulser et al. 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.


The main result is that if the translation complement of a translation plane of order q2 contains a group isomorphic to SL(2,q) and if the subgroups of order q are elations (shears), then the plane is Desarguesian. This generalizes earlier work of Walker, who assumed that the kernel of the plane contained GF(q).