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

Abstract

Using geometric methods and without invoking deep results from group theory, we prove that a classical unital of even order $n\ge 4$ 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 $1$.