A characterization of the desarguesian planes of order q2 by SL(2,q) - D. A. Foulser; N. L. Johnson; T. G. Ostrom (International Journal of Mathematics and Mathematical Sciences)
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).