Skip to main content
SpringerLink
Log in

The non-existence of certain regular generalized polygons

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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

References

  1. T. Grundhöfer andH. Van Maldeghem, Topological polygons and affine buildings of rank three. Atti Sem. Mat. Fis. Univ. Modena38, 459–474 (1990).

    Google Scholar 

  2. J. R.Faulkner, Steinberg relations and coordinatization of polygonal geometries. Mem. Amer. Math. Soc.185 (1977).

  3. W. Feit andG. Higman, The non-existence of certain generalized polygons. J. Algebra1, 114–131 (1964).

    Google Scholar 

  4. M.Joswig and H. vanMaldeghem, An essay on the Ree octagons. To appear in J. Alg. Combin.

  5. N. Knarr, The nonexistence of certain topological polygons. Forum Math.2, 603–612 (1990).

    Google Scholar 

  6. S. E.Payne and J. A.Thas, Finite generalized quadrangles. Boston-London 1984.

  7. M. A. Ronan, A geometric characterization of Moufang hexagons. Invent. Math.57, 227–262 (1980).

    Google Scholar 

  8. J. Tits, Sur la trialité et certains groupes qui s' en déduisent. Publ. Math. IHES2, 14–60 (1959).

    Google Scholar 

  9. J.Tits, Buildings of spherical type and finite BN-pairs. LNM386, Berlin-Heidelberg-New York 1974.

  10. J. Tits, Classification of buildings of spherical type and Moufang polygons: a survey. Atti Convegni Lincei17, 229–246 (1976).

    Google Scholar 

  11. J. Tits, Spiegelungsgruppen, die als Weylgruppen auftreten. Invent Math.43, 283–295 (1977).

    Google Scholar 

  12. J. Tits, Non-existence de certains polygones généralisés I/II. Invent. Math.36, 275–284 (1976); Invent Math.51, 267–269 (1979).

    Google Scholar 

  13. J. Tits, Moufang octagons and the Ree groups of type2 F 4. Amer. J. Math.105, 539–594 (1983).

    Google Scholar 

  14. H. Van Maldeghem, Generalized polygons with valuation. Arch. Math.53, 513–520 (1989).

    Google Scholar 

  15. H.Van Maldeghem and I.Bloemen, Generalized hexagons as amalgamations of generalized quadrangles. To appear in European J. Combin.

  16. H.Van Maldeghem, The geometry of traces in Ree octagons. Preprint.

  17. R. Weiss, The nonexistence of certain Moufang polygons. Invent. Math.51, 261–266 (1979).

    Google Scholar 

Download references

Author information

Author notes

  1. H. Van Maldeghem

    Present address: Department of Pure Mathematics and Computer Algebra, University of Gent, Krijgslaan 281, B-9000, Gent, Belgium

Authors and Affiliations

    Authors
    1. H. Van Maldeghem
      View author publications

      You can also search for this author in PubMed Google Scholar

    Additional information

    Senior Research Associate at the National Fund for Scientific Research (Belgium)

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Van Maldeghem, H. The non-existence of certain regular generalized polygons. Arch. Math 64, 86–96 (1995). https://doi.org/10.1007/BF01193554

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01193554

    Keywords

    Search

    Navigation