Incidence Systems associated with Non-Planar Nearfields

Abstract

In [2] Sandler studied generalizations of projective planes called pseudo planes. These structures gave rise to ternary operations for which addition and multiplication are loop operations. Our aim in this paper is to investigate the pseudo planes for which the operations of addition and multiplication give rise to nearfields. The pseudo planes for which this is true will be called π-systems in this paper, and a list of postulates for such systems is given in § 2. In that section some results on collineations of π-systems are given which are stronger than analogous results for general pseudo planes.