, Volume 37, Issue 2, pp 283–311 | Cite as

Finite affine planes in projective spaces

Original Paper


We classify all representations of an arbitrary affine plane A of order q in a projective space PG(d,q) such that lines of A correspond with affine lines and/or plane q-arcs and such that for each plane q-arc which corresponds to a line L of A the plane of PG(d,q) spanned by the q-arc does not contain the image of any point off L of A.

Mathematics Subject Classification (2000)

05B25 05B05 51A30 51A45 51E15 51E20 51B99 


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  1. [1]
    J. W. P. Hirschfeld: Projective Geometries over Finite Fields, 2nd edition, Clarendon Press, Oxford Mathematical Monographs, 1998.MATHGoogle Scholar
  2. [2]
    J. W. P. Hirschfeld: Finite Projective Spaces of Three Dimensions, Clarendon Press, Oxford Mathematical Monographs, 1985.MATHGoogle Scholar
  3. [3]
    J. W. P. Hirschfeld and J. A. Thas: General Galois Geometries, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1991.MATHGoogle Scholar
  4. [4]
    S. E. Payne and J. A. Thas: Finite Generalized Quadrangles, Research Notes in Mathematics 110, Pitman Advanced Publishing Program, Boston/London/Melbourne, 1984; second edition in: EMS Series of Lectures in Mathematics, European Mathematical Society, 2009.Google Scholar
  5. [5]
    J. A. Thas, K. Thas and H. Van Maldeghem: Translation Generalized Quadran-gles, World Scientific Publishing, Hackensack, 2007.Google Scholar
  6. [6]
    J. A. Thas and H. Van Maldeghem: Characterizations of the finite quadric Veroneseans V n 2n, Quart. J. Math. 55 (2004), 99–113.CrossRefMATHGoogle Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsGhent UniversityGhentBelgium

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