## Innovations in Incidence Geometry

### A geometric proof of Wilbrink's characterization of even order classical unitals

Alice M. W. Hui

#### Abstract

Using geometric methods and without invoking deep results from group theory, we prove that a classical unital of even order $n≥4$ is characterized by two conditions (I) and (II): (I) is the absence of O’Nan configurations of four distinct lines intersecting in exactly six distinct points; (II) is a notion of parallelism. This was previously proven by Wilbrink (1983), where the proof depends on the classification of finite groups with a split BN-pair of rank $1$.

#### Article information

Source
Innov. Incidence Geom., Volume 15, Number 1 (2017), 145-167.

Dates
Received: 13 January 2015
Accepted: 24 February 2015
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323012

Digital Object Identifier
doi:10.2140/iig.2017.15.145

Mathematical Reviews number (MathSciNet)
MR3713359

Zentralblatt MATH identifier
06847112

#### Citation

Hui, Alice M. W. A geometric proof of Wilbrink's characterization of even order classical unitals. Innov. Incidence Geom. 15 (2017), no. 1, 145--167. doi:10.2140/iig.2017.15.145. https://projecteuclid.org/euclid.iig/1551323012

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