English

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 II is an inversive plane of even order qq then qq must be a power of two and II must be the incidence system of points versus plane ovals in an ovoid in the projective 33-space over the field of order qq. 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}
}