Unitals and Inversive Planes
Date
1997
Authors
Barwick, S.
O'Keefe, C.
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Journal article
Citation
Journal of Geometry, 1997; 58(1-2):43-52
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Abstract
We show that if U is a Buekenhout-Metz unital (with respect to a point P) in any translation plane of order q<sup>2</sup> with kernel containing GF(q), then U has an associated 2-(q<sup>2</sup>, 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.