Non-Desarguesian Projective Plane Geometries Which Satisfy The Harmonic Point Axiom

Source abstract

1. Introduction and summary. In her papers (12) and (13) R. Moufang discusses projective plane geometries which satisfy the axiom of the uniqueness of the fourth harmonic point. Her main result is that in such geometries non-homogeneous co-ordinates may be assigned to the points of the plane (except for the “line at infinity”) in such a way that straight lines have equations of the forms aαx + y + β = 0, or x + γ − 0.