Unitals and Inversive Planes

Abstract

We show that if U is a Buekenhout-Metz unital (with respect to a point P) in any translation plane of order q2 with kernel containing GF(q), then U has an associated 2-(q2, q + 1, q) design which is the point-residual of an inversive plane, generalizing results of Wilbrink, Baker and Ebert. Further, our proof gives a natural, geometric isomorphism between the resulting inversive plane and the (egglike) inversive plane arising from the ovoid involved in the construction of the Buekenhout-Metz unital. We apply our results to investigate some parallel classes and partitions of the set of blocks of any Buekenhout-Metz unital. © Birkhäuser Verlag, Basel, 1997.