Benz planes of Dembowski type and groups of tangential projectivities

Abstract

Using the tangential relation we introduce in Benz planes M of Dembowski type, which generalize the Benz planes over algebras of characteristic 2, the group Π of tangential perspectivities. We prove that these groups have the same behaviour as the classical groups of projectivities if any tangential perspectivity is induced by an automorphism of M. As permutation groups of a circle onto itself the groups Π essentially differs from the classical groups of projectivities. If M is a Laguerre plane of Dembowski type, then Π is always sharply 3-transitive. For Minkowski planes of Dembowski type Π is at least 2-transitive. If M is a finite Benz plane of order 2s, then Π is isomorphic to the group PGL2(2s) in its sharply 3-transitive representation.