On a theorem of Rigby View Full Text


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Article Info

DATE

2016-07

AUTHORS

Dieter Jungnickel

ABSTRACT

Let Δ=BAG(2,q) denote the classical biaffine plane of order q, that is, the symmetric ((q2-1)q) configuration obtained from the classical affine plane Σ=AG(2,q) of order q by omitting a point of Σ together with all lines through this point. Now let q≥4 be a power of a prime p and assume that Δ admits an embedding into the projective plane Π=PG(2,F), where F is a (not necessarily commutative) field. Then this embedding extends to a projective subplane Π0≅PG(2,q) of Π; in particular, F has characteristic p. Consequently, BAG(2,q) with q≥4 admits an embedding into PG(2,q′) if only if q′ is a power of q. This strengthens a result of Rigby (Canad J Math 17:977–1009, 1965) in a special case while simultaneously providing a more elegant proof. More... »

PAGES

257-265

References to SciGraph publications

  • 2013-07. New invariants for incidence structures in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1987-08. 83 inPG(2,q) in ARCHIV DER MATHEMATIK
  • 2012-12. The geometric dimension of some small configurations in JOURNAL OF GEOMETRY
  • 1975. Projektive Ebenen in NONE
  • Journal

    TITLE

    Journal of Geometry

    ISSUE

    2

    VOLUME

    107

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00022-015-0298-7

    DOI

    http://dx.doi.org/10.1007/s00022-015-0298-7

    DIMENSIONS

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