Dembowski's Theorem on Finite Inversive Planes of Even Order
Combinatorics
2023-03-06 v1
Abstract
A remarkable theorem due to Peter Dembowski states that if is an inversive plane of even order then must be a power of two and must be the incidence system of points versus plane ovals in an ovoid in the projective -space over the field of order . 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.
Keywords
Cite
@article{arxiv.2303.02013,
title = {Dembowski's Theorem on Finite Inversive Planes of Even Order},
author = {Bhaskar Bagchi},
journal= {arXiv preprint arXiv:2303.02013},
year = {2023}
}