Epimorphisms of Generalized Polygons, Part 2: Some Existence and Non-Existence Results

  • Ralf Gramlich
  • Hendrik Van Maldeghem
Part of the Developments in Mathematics book series (DEVM, volume 3)

Abstract

In Part 1 of this paper (see [7]), we studied the general theory of epimorphisms of generalized polygons, with emphasis on epimorphisms that do not preserve the diameter. Let us briefly recall the situation and relevant definitions.

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References

  1. [1]
    A. Blokhuis, personal communication.Google Scholar
  2. [2]
    R. Bödi and L. Kramer, On homomorphisms between generalized polygons, Geom. Dedicata 58 (1995), 1–14.MathSciNetCrossRefGoogle Scholar
  3. [3]
    A.E. Brouwer, A non-degenerate generalized quadrangle with lines of size four is finite, Advances in Finite Geometries and Designs, Proceedings of the Third Isle of Thorns Conference (eds. J.W.P. Hirschfeld et al.), Oxford University Press, Oxford, 1991, 47–49.Google Scholar
  4. [4]
    P.J. Cameron, Orbits of permutation groups on unordered sets, II., J. London Math. Soc. 23 (1981), 49–264.CrossRefGoogle Scholar
  5. [5]
    G. Cherlin, Notes on locally finite generalized quadrangles, 1996.Google Scholar
  6. [6]
    W. Feit and G. Higman, The nonexistence of certain generalized polygons, J. Algebra 1 (1964), 114–131.MathSciNetCrossRefGoogle Scholar
  7. [7]
    R. Gramlich and H. Van Maldeghem, Epimorphisms of generalized polygons, Part 1: geometrical characterizations, Des. Codes Cryptogr. 21 (2000), 99–111.MathSciNetCrossRefGoogle Scholar
  8. [8]
    W.H. Haemers and C. Roos, An inequality for generalized hexagons, Geom. Dedicata 10 (1981), 219–222.MathSciNetCrossRefGoogle Scholar
  9. [9]
    D.G. Higman, Invariant relations, coherent configurations and generalized polygons, Combinatorics (eds. M. Hall and J.H. Van Lint), Proceedings ofthe Advanced Study Institute, Breukelen, 1974, Part 3: Combinatorial Group Theory, Reidel, Dordrecht, 1975, 347–363.Google Scholar
  10. [10]
    S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, London, 1984.Google Scholar
  11. [11]
    J. Tits, Sur la trialité et certains groupes qui s’en déduisent, Inst. Hautes Études Sci. Publ. Math. 2 (1959), 13–60.CrossRefGoogle Scholar
  12. [12]
    J. Tits, Endliche Spiegelungsgruppen, die als Weylgruppen auftreten, Invent. Math. 43 (1977), 283–295.MathSciNetCrossRefGoogle Scholar
  13. [13]
    H. Van Maldeghem, Generalized Polygons, Birkhäuser, Basel 1998.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Ralf Gramlich
    • 1
  • Hendrik Van Maldeghem
    • 2
  1. 1.Vakgroep Discrete WiskundeTU EindhovenEindhovenThe Netherlands
  2. 2.Vakgroep Zuivere Wiskunde en ComputeralgebraUniversiteit GentGentBelgium

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