The Uniqueness of the Actions of Certain Branch Groups on Rooted Trees

Geometriae Dedicata

Volumn 100, Issue 1, 2003, Pages 103-116

  Grigorchuk, R I ^a   Wilson, J S ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Basal subgroups; Group actions; Rooted trees; Vertex subgroups

Indexed keywords

EID: 0347756665     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025851804561     Document Type: Article

References (28)

1. Bartholdi, L. and Grigorchuk, R. I.: Sous-groups paraboliques et représentations de groupes branchés, C.R. Acad. Sci. Paris Sér. I Math. 332 (2001), 789-794.
2. Bass, H. and Kulkarni, R.: Uniform tree lattices, J. Amer. Math. Soc. 3 (1990), 843-902.
3. Bass, H. and Lubotzky, A.: Rigidity of group actions on locally finite trees, Proc. London Math. Soc. (3) 69 (1994), 541-575.
4. Grigorchuk, R. I.: On the Burnside problem for periodic groups, Funktsional. Anal. i Prilozhen. 14 (1980), 53-54. (English translation: Functional Anal. Appl. 14 (1980), 53-54.)
5. Grigorchuk, R. I.: On the Burnside problem for periodic groups, Funktsional. Anal. i Prilozhen. 14 (1980), 53-54. (English translation: Functional Anal. Appl. 14 (1980), 53-54.)
6. Grigorchuk, R. I.: On the Milnor problem of group growth, Dokl. Akad. Nauk SSSR 271 (1983), 30-33. (English translation: Soviet Math. Dokl. 28 (1983), 23-26.)
7. Grigorchuk, R. I.: On the Milnor problem of group growth, Dokl. Akad. Nauk SSSR 271 (1983), 30-33. (English translation: Soviet Math. Dokl. 28 (1983), 23-26.)
8. Grigorchuk, R. I.: The growth degrees of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk. SSSR. Ser. Mat. 48 (1984), 939-985. (English translation: Math. SSSR. Izv. 25 (1985).)
9. Grigorchuk, R. I.: The growth degrees of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk. SSSR. Ser. Mat. 48 (1984), 939-985. (English translation: Math. SSSR. Izv. 25 (1985).)
10. Grigorchuk, R. I.: On the growth degrees of p-groups and torsion-free groups, Math. Sb. 126 (1985), 194-214. (English translation: Math. USSR Sbornik 54 (1986), 185-205.)
11. Grigorchuk, R. I.: On the growth degrees of p-groups and torsion-free groups, Math. Sb. 126 (1985), 194-214. (English translation: Math. USSR Sbornik 54 (1986), 185-205.)
12. Grigorchuk, R. I.: A relationship between algorithmic problems and entropy characteristics of groups, Dokl. Akad. Nauk SSSR 284 (1985), 24-29. (English translation: Soviet Math. Dokl. 32 (1985), 356-360.)
13. Grigorchuk, R. I.: A relationship between algorithmic problems and entropy characteristics of groups, Dokl. Akad. Nauk SSSR 284 (1985), 24-29. (English translation: Soviet Math. Dokl. 32 (1985), 356-360.)
14. Grigorchuk, R. I.: On the Hilbert-Poincaré series of graded algebras associated with groups, Math. Sb. 180 (1989), 207-225. (English translation: Math. USSR Sbornik 66 (1990), 211-229.)
15. Grigorchuk, R. I.: On the Hilbert-Poincaré series of graded algebras associated with groups, Math. Sb. 180 (1989), 207-225. (English translation: Math. USSR Sbornik 66 (1990), 211-229.)
16. Grigorchuk, R. I.: Just infinite branch groups, In: New Horizons in Pro-p Groups, Birkhäuser, Basel, 2000, pp. 121-179.
17. Grigorchuk, R. I. and Wilson, J. S.: A rigidity property concerning abstract commensurability of subgroups, J. London Math. Soc., to appear.
18. Gupta, N. and Sidki, S.: On the Burnside problem for periodic groups, Math. Z. 182 (1983), 385-388.
19. Gupta, N. and Sidki, S.: Some infinite p-groups, Algebra i Logika 22 (1983), 584-589. (Algebra and Logic 22 (1983), 421-424.)
20. Gupta, N. and Sidki, S.: Some infinite p-groups, Algebra i Logika 22 (1983), 584-589. (Algebra and Logic 22 (1983), 421-424.)
21. de la Harpe, P.: Topics in Geometric Group Theory, Univ. Chicago Press, 2000.
22. Lubotzky, A. Mozes, S. and Zimmer, R. J.: Superrigidity for the commensurability group of tree lattices, Comment. Math. Helv. 69 (1994), 523-548.
23. Lavreniuk, Y. and Nekrashevich, V.: Rigidity of branch groups acting on rooted trees, Geom. Dedicata 89 (2002), 155-175.
24. Margulis, G. A.: Discrete Subgroups of Semisimple Lie Groups, Springer, New York, 1991.
25. Rubin, M.: The Reconstruction of Trees from their Automorphism Groups, Amer. Math. Soc. 1993.
26. Sidki, S. N.: On a 2-generated infinite 3-group: subgroups and automorphisms, J. Algebra 110 (1987), 24-55.
27. Wilson, J. S.: Groups with every proper quotient finite, Proc. Cambridge Philos. Soc. 69 (1971), 373-391.
28. Wilson, J. S.: On just infinite abstract and profinite groups, In: New Horizons in Pro-p Groups, Birkhäuser, Basel, 2000, pp. 181-203.