Vol. 15, No. 1, 2017

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

Alice M. W. Hui

Vol. 15 (2017), No. 1, 145–167
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.

Keywords
unital, classical unital, Hermitian curve, spread
Mathematical Subject Classification 2010
Primary: 05B25, 05B25, 51E20, 51E21, 51E23
Milestones
Received: 13 January 2015
Accepted: 24 February 2015
Authors
Alice M. W. Hui