Skip to main content
Log in

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson,Atlas of finite groups, Oxford, Clarendon Press, 1985.

    MATH  Google Scholar 

  2. A. Borel, J. Tits, Homomorphismes “abstraits” de groupes algébriques simples,Ann. of Math. 97 (1973), 499–571.

    Article  MathSciNet  Google Scholar 

  3. A. E. Brouwer, A. M. Cohen, A. Neumaier,Distance Regular Graphs, Ergebnisse, 3. Folge, Band 18, Springer 1989.

  4. M. Burger, S. Mozes, Finitely presented simple groups and products of trees,C.R. Acad. Sci. Paris, t.324, Serie I, 1997, p. 747–752.

    MATH  MathSciNet  Google Scholar 

  5. M. Burger, S. Mozes, Lattices in products of trees,Publ. Math. IHES 92 (2001), 151–194.

    Google Scholar 

  6. M. Burger, S. Mozes, R. Zimmer, Linear representations and arithmeticity for lattices in products of trees, in preparation.

  7. H. Bass, A. Lubotzky, Tree lattices, Progr. Math.176 (2001), Birkhäuser.

  8. H. Bass, R. Kulkarni, Uniform tree lattices,J. Amer. Math. Soc. 3 (1990), 843–902.

    Article  MATH  MathSciNet  Google Scholar 

  9. W. Ballmann, M. Gromov, V. Schroeder, Manifolds of nonpositive curvature,Progr. Math. 61 (1985), Birkhäuser.

  10. P. J. Cameron, Permutation groups inHandbook of Combinatorics, R. L. Graham, M. Grötschel, L. Lovász (eds), Elsevier, 1995, vol.I, 611–646.

    Google Scholar 

  11. J. D. Dixon, B. Mortimer, Permutation Groups,Graduate Texts in Mathematics 163, Springer 1996.

  12. A. Figa-Talamanca, C. Nebbia, Harmonic analysis and representation theory for groups acting on homogeneous trees.LMS Lecture Notes Series 162, Cambridge Univ. Press, 1991.

  13. D. Goldschmidt, Automorphisms of trivalent graphs,Ann. Math. 111 (1980), 377–406.

    Article  MathSciNet  Google Scholar 

  14. A. Lubotzky, Tree lattices and lattices in Lie groups, inCombinatorial and geometric group theory, Edinburgh 1993,LMS Lecture Notes Series 204 (1995), 217–232.

    MathSciNet  Google Scholar 

  15. A. Lubotzky, S. Mozes, R. J. Zimmer, Superrigidity of the commensurability group of tree lattices,Comment. Math. Helv. 69 (1994), 523–548.

    Article  MATH  MathSciNet  Google Scholar 

  16. C. Nebbia, Groups of isometries of a tree and the Kunze-Stein phenomenon,Pacific Journal of Mathematics, Vol.133, No. 1, 1988.

  17. Ch. E. Praeger, Finite quasiprimitive graphs inSurveys in Combinatorics, 1997, Proc. of the 16th British combinatorial conference, London UK, July 1997. London: Cambridge University Press,Lond. Math. Soc. LNS 241 (1997), 65–85.

    Google Scholar 

  18. J. P. Serre,Trees, Springer 1980.

  19. J. G. Thompson, Bounds for orders of maximal subgroups,J. Algebra 14 (1970), 135–138.

    Article  MATH  MathSciNet  Google Scholar 

  20. J. Tits, Algebraic and abstract simple groups,Ann. of Math. 80 (1964), 313–329.

    Article  MathSciNet  Google Scholar 

  21. J. Tits, Sur le groupe des automorphismes d’un arbre inEssays on Topology and Related Topics: Mémoires dédiés à Georges de Rham, A. Haefliger, R. Narasimhan (eds), Berlin and New York, Springer-Verlag (1970), 188–211.

    Google Scholar 

  22. W. T. Tutte, A family of cubical graphs,Proc. Cambridge Phil. Soc. 43 (1947), 459–474.

    Article  MATH  MathSciNet  Google Scholar 

  23. R. Weiss, Generalized polygons ands-transitive graphs inFinite Geometries Buildings and Related Topics, W. M. Kantor, R. A. Liebler, S. E. Payne, E. E. Shult (eds) Oxford, Clarendon Press (1990), 95–103.

    Google Scholar 

  24. H. Wielandt, Subnormal Subgroups and Permutation Groups,Ohio State University Lecture Notes (1971), Columbus.

  25. J. S. Wilson, Profinite Groups,London Math. Soc. monographs 19 (1998), Oxford science publications.

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Burger, M., Mozes, S. Groups acting on trees: From local to global structure. Publications Mathématiques de L’Institut des Hautes Scientifiques 92, 113–150 (2000). https://doi.org/10.1007/BF02698915

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02698915

Keywords

Navigation