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Unitals and inversive planes

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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 2 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.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Adelaide, 5005, Adelaide, Australia

    S. G. Barwick & Christine M. O'Keefe

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  1. S. G. Barwick
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  2. Christine M. O'Keefe
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Barwick, S.G., O'Keefe, C.M. Unitals and inversive planes. J Geom 58, 43–52 (1997). https://doi.org/10.1007/BF01222925

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  • DOI: https://doi.org/10.1007/BF01222925

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