Dembowski's Theorem on Finite Inversive Planes of Even Order

Abstract

A remarkable theorem due to Peter Dembowski states that if $I$ is an inversive plane of even order $q$ then $q$ must be a power of two and $I$ must be the incidence system of points versus plane ovals in an ovoid in the projective $3$-space over the field of order $q$. In this paper we present a short and self-contained proof of this result. Our proof depends on the classification due to Benson of the symmetric and regular finite generalized quadrangles. Included here is a deduction of Benson's Theorem from the Dembowski-Wagner combinatorial characterization of finite projective geometries.