Groups acting on trees : from local to global structure

Marc Burger; Shahar Mozes

Publications Mathématiques de l'IHÉS (2000)

  • Volume: 92, page 113-150
  • ISSN: 0073-8301

How to cite

top

Burger, Marc, and Mozes, Shahar. "Groups acting on trees : from local to global structure." Publications Mathématiques de l'IHÉS 92 (2000): 113-150. <http://eudml.org/doc/104168>.

@article{Burger2000,
author = {Burger, Marc, Mozes, Shahar},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {locally finite tree; group of automorphisms; Bruhat-Tits tree; locally primitive group; vertex transitive groups},
language = {eng},
pages = {113-150},
publisher = {Institut des Hautes Études Scientifiques},
title = {Groups acting on trees : from local to global structure},
url = {http://eudml.org/doc/104168},
volume = {92},
year = {2000},
}

TY - JOUR
AU - Burger, Marc
AU - Mozes, Shahar
TI - Groups acting on trees : from local to global structure
JO - Publications Mathématiques de l'IHÉS
PY - 2000
PB - Institut des Hautes Études Scientifiques
VL - 92
SP - 113
EP - 150
LA - eng
KW - locally finite tree; group of automorphisms; Bruhat-Tits tree; locally primitive group; vertex transitive groups
UR - http://eudml.org/doc/104168
ER -

References

top
  1. [At] J. H. CONWAY, R. T. CURTIS, S. P. NORTON, R. A. PARKER, R. A. WILSON, Atlas of finite groups, Oxford, Clarendon Press, 1985. Zbl0568.20001MR88g:20025
  2. [Bo-Ti] A. BOREL, J. TITS, Homomorphismes "abstraits" de groupes algébriques simples, Ann. of Math. 97 (1973), 499-571. Zbl0272.14013MR47 #5134
  3. [B-C-N] A. E. BROUWER, A. M. COHEN, A. NEUMAIER, Distance Regular Graphs, Ergebnisse, 3. Folge, Band 18, Springer 1989. Zbl0747.05073MR90e:05001
  4. [B-M]1 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. Zbl0966.20013MR98g:20041
  5. [B-M]2 M. BURGER, S. MOZES, Lattices in products of trees, Publ. Math. IHES 92 (2001), 151-194. Zbl1007.22013MR2002i:20042
  6. [B-M-Z] M. BURGER, S. MOZES, R. ZIMMER, Linear representations and arithmeticity for lattices in products of trees, in preparation. Zbl1198.22007
  7. [Ba-Lu] H. BASS, A. LUBOTZKY, Tree lattices, Progr. Math. 176 (2001), Birkhäuser. Zbl1053.20026MR2001k:20056
  8. [Ba-Ku] H. BASS, R. KULKARNI, Uniform tree lattices, J. Amer. Math. Soc. 3 (1990), 843-902. Zbl0734.05052MR91k:20034
  9. [Bal-G-S] W. BALLMANN, M. GROMOV, V. SCHROEDER, Manifolds of nonpositive curvature, Progr. Math. 61 (1985), Birkhäuser. Zbl0591.53001MR87h:53050
  10. [Ca] P. J. CAMERON, Permutation groups in Handbook of Combinatorics, R. L. Graham, M. Grötschel, L. Lovász (eds), Elsevier, 1995, vol. I, 611-646. Zbl0845.20001MR97e:20002
  11. [Di-Mo] J. D. DIXON, B. MORTIMER, Permutation Groups, Graduate Texts in Mathematics 163, Springer 1996. Zbl0951.20001MR98m:20003
  12. [F-Ne] A. FIGA-TALAMANGA, C. NEBBIA, Harmonic analysis and representation theory for groups acting on homogeneous trees. LMS Lecture Notes Series 162, Cambridge Univ. Press, 1991. Zbl1154.22301MR93f:22004
  13. [Go] D. GOLDSCHMIDT, Automorphisms of trivalent graphs, Ann. Math. 111 (1980), 377-406. Zbl0475.05043MR82a:05052
  14. [Lu] A. LUBOTZKY, Tree lattices and lattices in Lie groups, in Combinatorial and geometric group theory, Edinburgh 1993, LMS Lecture Notes Series 204 (1995), 217-232. Zbl0840.22019MR1320284
  15. [L-M-Z] A. LUBOTZKY, S. MOZES, R. J. ZIMMER, Superrigidity of the commensurability group of tree lattices, Comment. Math. Helv. 69 (1994), 523-548. Zbl0839.22011MR96a:20032
  16. [Ne] C. NEBBIA, Groups of isometries of a tree and the Kunze-Stein phenomenon, Pacific Journal of Mathematics, Vol. 133, No. 1, 1988. Zbl0646.43006MR89h:43005
  17. [Pr] Ch. E. PRAEGER, Finite quasiprimitive graphs in Surveys 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. Zbl0881.05055
  18. [Se] J. P. SERRE, Trees, Springer 1980. Zbl0548.20018MR82c:20083
  19. [Th] J. G. THOMPSON, Bounds for orders of maximal subgroups, J. Algebra 14 (1970), 135-138. Zbl0221.20031MR40 #5720
  20. [Ti]1 J. TITS, Algebraic and abstract simple groups, Ann. of Math. 80 (1964), 313-329. Zbl0131.26501MR29 #2259
  21. [Ti]2 J. TITS, Sur le groupe des automorphismes d'un arbre in Essays 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. Zbl0214.51301MR45 #8582
  22. [Tu] W. T. TUTTE, A family of cubical graphs, Proc. Cambridge Phil. Soc. 43 (1947), 459-474. Zbl0029.42401MR9,97g
  23. [We] R. WEISS, Generalized polygons and s-transitive graphs in Finite Geometries Buildings and Related Topics, W. M. Kantor, R. A. Liebler, S. E. Payne, E. E. Shult (eds) Oxford, Clarendon Press (1990), 95-103. Zbl0751.05051MR91j:51011
  24. [Wi] H. WIELANDT, Subnormal Subgroups and Permutation Groups, Ohio State University Lecture Notes (1971), Columbus. 
  25. [Wil] J. S. WILSON, Profinite Groups, London Math. Soc. monographs 19 (1998), Oxford science publications. Zbl0909.20001MR2000j:20048

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.