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  • 1
    Electronic Resource
    Electronic Resource
    A characterization of the classical unital (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 175-180 
    Details
    ISSN: 1572-9168
    Keywords: 51E20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We define Buekenhout unitals in derivable translation planes of dimension 2 over their kernel and provide a characterization of these unitals. We use this result to improve the characterization of classical unitals given by Lefèvre-Percsy [13] and Faina and Korchmáros [7].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01263605
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  • 2
    Electronic Resource
    Electronic Resource
    Unitals in the Hall plane (1997)
    Springer
    Journal of geometry 58 (1997), S. 26-42 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The unitals in the Hall plane are studied by deriving PG(2,q 2)and observing the effect on the unitals of PG(2,q 2).The number of Buekenhout and Buekenhout-Metz unitals in the Hall plane is determined. As a corollary we show that the classical unital is not embeddble in the Hall plane as a Buekenhout unital and that the Buekenhout unitals of H(q 2)are not embeddable as Buekenhout unitals in the Desarguesian plane. Finally, we generalize this technique to other translation planes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222924
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  • 3
    Electronic Resource
    Electronic Resource
    Unitals and inversive planes (1997)
    Springer
    Journal of geometry 58 (1997), S. 43-52 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222925
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Unitals which meet Baer subplanes in 1 moduloq points (2000)
    Springer
    Journal of geometry 68 (2000), S. 16-22 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that a parabolic unitalU in a translation plane π of orderq 2 with kernel containing GF(q) is a Buekenhout-Metz unital if and only if certain Baer subplanes containing the translation line of π meetU in 1 moduloq points. As a corollary we show that a unital 16-03 in PG(2,q 2) is classical if and only if it meets each Baer subplane of PG(2,q 2) in 1 moduloq points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01221057
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