International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 605-608
doi:10.1155/S0161171283000551
A characterization of the desarguesian planes of order q2 by SL(2,q)
D.A. Foulser1
, N.L. Johnson2
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
Abstract
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).