Skip to main content
SpringerLink
Log in

Generalized quadrangles of order (q, q 2),q even, containingW(q) as a subquadrangle

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

In this paper we give a characterization of the generalized quadrangleQ(5,q),q even, in terms of ovoids of its subquadrangles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bagchi, B. and Sastry, N. S. N.: Even order inversive planes, generalized quadrangles and codes,Geom. Dedicata 22 (1987), 137–147.

    Google Scholar 

  2. Bagchi, B. and Sastry, N. S. N.: Intersection patterns of the classical ovoids in sympletic 3-space of even order,J. Algebra 126 (1989), 147–160.

    Google Scholar 

  3. Barlotti, A.: Some topics in finite geometrical structures,Institute of Statistics Mimeo Series, No. 439, University of North Carolina, 1965.

  4. Baer, R.:Linear Algebra and Projective Geometry, Academic Press, New York, 1952.

    Google Scholar 

  5. Fellegara, G.: Gli ovaloidi di uno spazio tredimensionale di Galois di ordine 8,Atti Accad. Naz. Lincei Rend. 32 (1962), 170–176.

    Google Scholar 

  6. Hirschfeld, J. W. P.:Finite Projective Spaces of Three Dimensions, Clarendon Press, Oxford, 1985.

    Google Scholar 

  7. O'Keefe, C. M.: Ovoids in PG(3,q): a survey,Discrete Math. (to appear).

  8. O'Keefe, C. M. and Penttila, T.: Ovoids of PG(3, 16) are elliptic quadrics, II,J. Geometry 44 (1992), 140–159.

    Google Scholar 

  9. O'Keefe, C. M., Penttila, T. and Royle, G. F.: Classification of ovoids in PG(3, 32),J. Geom. 50 (1994), 143–150.

    Google Scholar 

  10. Payne, S. E. and Thas, J. A.:Finite Generalized Quadrangles. Pitman, London, 1984.

    Google Scholar 

  11. Penttila, T.: Personal communication, 1993.

  12. Segre, B.: Introduction to Galois geometries,Mem. Acad. Naz. Lincei 8 (1967), 137–236.

    Google Scholar 

  13. Taylor, D. E.:The Geometry of the Classical Groups, Heldermann Verlag, Berlin, 1992.

    Google Scholar 

  14. Thas, J. A.: A remark concerning the restriction on the parameters of a 4-gonal subconfiguration,Simon Stevin 48 (1974–75), 65–68.

    Google Scholar 

  15. Thas, J. A. and Payne, S. E.: Spreads and ovoids in finite generalized quadrangles,Geom. Dedicata 52 (1994), 227–253.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Matthew R. Brown

Authors
  1. Matthew R. Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brown, M.R. Generalized quadrangles of order (q, q 2),q even, containingW(q) as a subquadrangle. Geom Dedicata 56, 299–306 (1995). https://doi.org/10.1007/BF01263571

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01263571

Mathematics Subject Classification (1991)

Search

Navigation