The Nonexistence of Certain Finite Projective Planes

Abstract

A projective plane geometry π is a mathematical system composed of undefined elements called points and undefined sets of points (at least two in number) called lines, subject to the following three postulates: (P 1 ) Two distinct points are contained in a unique line. (P 2 ) Two distinct lines contain a unique common point. (P 3 ) Each line contains at least three points.