A Classification of Semi-Translation Planes

Abstract

The classification of certain types of projective planes has recently been of considerable interest to both geometers and group theorists. Due in part to the current general interest in finite mathematics and the developments connecting group theory and finite geometry, the Lenz-Barlotti classification of finite projective planes (2; 10), in particular, has generated a tremendous amount of research. A great deal of this research has been related to the construction of non-Desarguesian planes.Fryxell (6), Hughes (7), Luneburg (11), and Ostrom (13; 15; 18) have found examples of projective planes, all of which are of a general type that we call semi-translation planes. Many of these planes are of the same Lenz-Barlotti class I-1. (The Lùneburg planes are translation planes. However, the planes dual to the Luneburg planes are semi-translation planes as well as dual translation planes.)