The Hall plane of order 9-revisited

Abstract

It is shown that the Hall plane of order 9 admits a collineation group isomorphic to SL(2,3) generated by Baer 3-collineations, whose Baer axes are disjoint as subspaces, where the union of whose components completely cover the components of the Hall plane. This group acts doubly transitive on a set of four points on the line at infinity of the plane.