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Volumn 248, Issue , 2005, Pages 117-218

Solved and unsolved problems around one group

Author keywords

Amenability; Branch groups; C* algebra; Contracting groups; Groups of finite type; Hecke type operator; Intermediate growth; Kolmogorov complexity; Markov operator; Maximal subgroups; Rational maps; Rooted trees; Schreier graphs; Self similar groups; Spectrum; Topology in the space of groups; Torsion groups; Trace; Weakly maximal subgroups

Indexed keywords


EID: 85027989810     PISSN: 07431643     EISSN: 2296505X     Source Type: Book Series    
DOI: 10.1007/3-7643-7447-0_5     Document Type: Chapter
Times cited : (123)

References (158)
  • 1
    • 0003470665 scopus 로고
    • Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas]. Springer-Verlag, Berlin
    • [Adi79] S. I. Adian. The Burnside problem and identities in groups, volume 95 of Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas]. Springer-Verlag, Berlin, 1979.
    • (1979) The Burnside Problem and Identities in Groups , vol.95
    • Adian, S.I.1
  • 2
    • 12344251397 scopus 로고    scopus 로고
    • Random walks on free periodic groups
    • [Adi82] S. I. Adian. Random walks on free periodic groups. Izv. Akad. Nauk SSSR Ser. Mat., 46(6):1139–1149,
    • Izv. Akad. Nauk SSSR Ser. Mat. , vol.46 , Issue.6 , pp. 1139-1149
    • Adian, S.I.1
  • 6
    • 13544268631 scopus 로고    scopus 로고
    • Dimension and randomness in groups acting on rooted trees
    • available at
    • [AV05] M. Abert and B. Virag. Dimension and randomness in groups acting on rooted trees. J. Amer. Math. Soc., 18(1):157–192, 2005. (available at http://www.arxiv.org/abs/math.GR/0212191).
    • (2005) J. Amer. Math. Soc. , vol.18 , Issue.1 , pp. 157-192
    • Abert, M.1    Virag, B.2
  • 7
    • 0010160553 scopus 로고
    • The Banach mean on groups. Uspehi Mat
    • The Banach mean on groups. Uspehi Mat. Nauk (N.S.), 12(6(78)):131–136, 1957.
    • (1957) Nauk (N.S.), 12(6(78)) , pp. 131-136
  • 8
    • 1842791216 scopus 로고    scopus 로고
    • The growth of Grigorchuk’s torsion group
    • [Bar98] L. Bartholdi. The growth of Grigorchuk’s torsion group. Internat. Math. Res. Notices, (20):1049–1054, 1998.
    • (1998) Internat. Math. Res. Notices , vol.20 , pp. 1049-1054
    • Bartholdi, L.1
  • 9
    • 0035579510 scopus 로고    scopus 로고
    • Lower bounds on the growth of a group acting on the binary rooted tree
    • [Bar01] L. Bartholdi. Lower bounds on the growth of a group acting on the binary rooted tree. Internat. J. Algebra Comput., 11(1):73–88, 2001.
    • (2001) Internat. J. Algebra Comput. , vol.11 , Issue.1 , pp. 73-88
    • Bartholdi, L.1
  • 10
    • 0242425107 scopus 로고    scopus 로고
    • Endomorphic presentations of branch groups
    • [Bar03] L. Bartholdi. Endomorphic presentations of branch groups. J. Algebra, 268(2):419–443, 2003.
    • (2003) J. Algebra , vol.268 , Issue.2 , pp. 419-443
    • Bartholdi, L.1
  • 11
    • 18844410779 scopus 로고    scopus 로고
    • Lie algebras and growth in branch groups
    • [Bar05] L. Bartholdi. Lie algebras and growth in branch groups. Pacific J. Math., 218(2):241–282, 2005.
    • (2005) Pacific J. Math. , vol.218 , Issue.2 , pp. 241-282
    • Bartholdi, L.1
  • 12
    • 0004168675 scopus 로고
    • Lectures in Mathematics ETH Zürich.¨ Birkhauser¨ Verlag, Basel
    • Topics in combinatorial group theory. Lectures in Mathematics ETH Zürich.¨ Birkhauser¨ Verlag, Basel, 1993.
    • (1993) Topics in Combinatorial Group Theory
  • 13
    • 85027997661 scopus 로고
    • Some groups whose reduced C -algebra is simple. Inst. Hautes Études Sci
    • ∗ -algebra is simple. Inst. Hautes Études Sci. Publ. Math., (80):117–134 (1995), 1994.
    • (1995) Publ. Math., (80) , vol.117-134 , pp. 1994
  • 16
    • 0007279035 scopus 로고    scopus 로고
    • On the spectrum of Hecke type operators related to some fractal groups
    • On the spectrum of Hecke type operators related to some fractal groups. Tr. Mat. Inst. Steklova, 231:5–45, 2000.
    • (2000) Tr. Mat. Inst. Steklova , vol.231 , pp. 5-45
  • 17
    • 0034664356 scopus 로고    scopus 로고
    • Bartholdi and R. I. Grigorchuk. Spectra of non-commutative dynamical systems and graphs related to fractal groups. C
    • Bartholdi and R. I. Grigorchuk. Spectra of non-commutative dynamical systems and graphs related to fractal groups. C. R. Acad. Sci. Paris S´r. I Math., 331(6):429–434, 2000.
    • (2000) R. Acad. Sci. Paris S´r. I Math. , vol.331 , Issue.6 , pp. 429-434
  • 18
    • 0242396640 scopus 로고    scopus 로고
    • On parabolic subgroups and Hecke algebras of some fractal groups
    • [BG02a] L. Bartholdi and R. I. Grigorchuk. On parabolic subgroups and Hecke algebras of some fractal groups. Serdica Math. J., 28(1):47–90, 2002.
    • (2002) Serdica Math. J. , vol.28 , Issue.1 , pp. 47-90
    • Bartholdi, L.1    Grigorchuk, R.I.2
  • 19
    • 0036507090 scopus 로고    scopus 로고
    • Context-free languages of sub-exponential growth
    • [BG02b] M. R. Bridson and R. H. Gilman. Context-free languages of sub-exponential growth. J. Comput. System Sci., 64(2):308–310, 2002.
    • (2002) J. Comput. System Sci. , vol.64 , Issue.2 , pp. 308-310
    • Bridson, M.R.1    Gilman, R.H.2
  • 21
    • 30344472506 scopus 로고    scopus 로고
    • Branch groups
    • North-Holland, Amsterdam
    • Branch groups. In Handbook of algebra, Vol. 3, pages 989–1112. North-Holland, Amsterdam, 2003.
    • (2003) Handbook of Algebra, Vol. 3 , pp. 989-1112
  • 26
    • 0010294077 scopus 로고    scopus 로고
    • Boston. P-adic Galois representations and pro-p Galois groups
    • Birkhauser¨ Boston, Boston, MA
    • Boston. p-adic Galois representations and pro-p Galois groups. In New horizons in pro-p groups, volume 184 of Progr. Math., pages 329–348. Birkhauser¨ Boston, Boston, MA, 2000.
    • (2000) New Horizons in Pro-P Groups, Volume 184 of Progr. Math. , pp. 329-348
  • 27
    • 0002632685 scopus 로고
    • Subgroups of direct products of free groups. J
    • [BR84] G. Baumslag and J. E. Roseblade. Subgroups of direct products of free groups. J. London Math. Soc. (2), 30(1):44–52, 1984.
    • (1984) London Math. Soc. (2) , vol.30 , Issue.1 , pp. 44-52
    • Baumslag, G.1    Roseblade, J.E.2
  • 28
    • 0035594954 scopus 로고    scopus 로고
    • On the word and period growth of some groups of tree automorphisms
    • [BŠ01] L. Bartholdi and Z. Šuniḱ. On the word and period growth of some groups of tree automorphisms. Comm. Algebra, 29(11):4923–4964, 2001.
    • (2001) Comm. Algebra , vol.29 , Issue.11 , pp. 4923-4964
    • Bartholdi, L.1    Šuniḱ, Z.2
  • 30
    • 22644451542 scopus 로고    scopus 로고
    • V H complexes, towers and subgroups of F × F
    • [BW99] M. R. Bridson and D. T. Wise. V H complexes, towers and subgroups of F × F. Math. Proc. Cambridge Philos. Soc., 126(3):481–497, 1999.
    • (1999) Math. Proc. Cambridge Philos. Soc. , vol.126 , Issue.3 , pp. 481-497
    • Bridson, M.R.1    Wise, D.T.2
  • 32
    • 85027990597 scopus 로고
    • Champetier. Properiét´ ´es g´en´eriques des groupes de type fini. The`se de doctorat
    • Champetier. Properiét´ ´es g´en´eriques des groupes de type fini. The`se de doctorat, Université´ de Lyon I, 1991.
    • (1991) Université´ De Lyon , pp. 1
  • 33
    • 0034216366 scopus 로고    scopus 로고
    • L’espace des groupes de type fini
    • [Cha00] C. Champetier. L’espace des groupes de type fini. Topology, 39(4):657–680, 2000.
    • (2000) Topology , vol.39 , Issue.4 , pp. 657-680
    • Champetier, C.1
  • 34
    • 84972502518 scopus 로고
    • Elementary amenable groups. Illinois
    • Elementary amenable groups. Illinois J. Math., 24(3):396–407, 1980.
    • (1980) J. Math. , vol.24 , Issue.3 , pp. 396-407
  • 35
    • 85027971076 scopus 로고    scopus 로고
    • Published for the Conference Board of the Mathematical Sciences, Washington, DC
    • CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1997.
    • (1997) CBMS Regional Conference Series in Mathematics
  • 36
    • 0003622025 scopus 로고
    • Studies in the History of Mathematics and Physical Sciences. Springer-Verlag, New York
    • [CM82] B. Chandler and W. Magnus. The history of combinatorial group theory, volume 9 of Studies in the History of Mathematics and Physical Sciences. Springer-Verlag, New York, 1982.
    • (1982) The History of Combinatorial Group Theory , vol.9
    • Chandler, B.1    Magnus, W.2
  • 39
    • 44249113894 scopus 로고    scopus 로고
    • A. Machì,` and F. Scarabotti. The Grigorchuk group of intermediate growth. Rend. Circ. Mat
    • [CSMS01] T. Ceccherini-Silberstein, A. Machì,` and F. Scarabotti. The Grigorchuk group of intermediate growth. Rend. Circ. Mat. Palermo (2), 50(1):67–102, 2001.
    • (2001) Palermo (2) , vol.50 , Issue.1 , pp. 67-102
    • Ceccherini-Silberstein, T.1
  • 40
    • 85028022726 scopus 로고    scopus 로고
    • And Tolli F. Finite Gelfand pairs and their applications to probability and statistics
    • [CSSFa] T. Ceccherini-Silberstein, F. Scarabotti, and Tolli F. Finite Gelfand pairs and their applications to probability and statistics. To appear.
    • To Appear.
    • Ceccherini-Silberstein, T.1    Scarabotti, F.2
  • 42
    • 84972490090 scopus 로고
    • Amenable semigroups
    • [Day57] M. M. Day. Amenable semigroups. Illinois J. Math., 1:509–544, 1957.
    • (1957) Illinois J. Math. , vol.1 , pp. 509-544
    • Day, M.M.1
  • 43
    • 0003730399 scopus 로고
    • Group representations in probability and statistics
    • Institute of Mathematical Statistics, Hayward, CA
    • Group representations in probability and statistics. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 11. Institute of Mathematical Statistics, Hayward, CA, 1988.
    • (1988) Institute of Mathematical Statistics Lecture Notes—Monograph Series , vol.11
  • 44
    • 0003572637 scopus 로고    scopus 로고
    • Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL
    • [dlH00] P. de la Harpe. Topics in geometric group theory. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000.
    • (2000) Topics in Geometric Group Theory
    • De La Harpe, P.1
  • 45
    • 60449085369 scopus 로고    scopus 로고
    • Mesures finiment additives et paradoxes
    • [dlH04] P. de la Harpe. Mesures finiment additives et paradoxes. Panoramas et Synthesis, 18:39–61, 2004.
    • (2004) Panoramas Et Synthesis , vol.18 , pp. 39-61
    • De La Harpe, P.1
  • 48
    • 0345865023 scopus 로고    scopus 로고
    • On isoperimetric profiles of finitely generated groups
    • [Ers03] A. Erschler. On isoperimetric profiles of finitely generated groups. Geom. Dedicata, 100:157–171, 2003.
    • (2003) Geom. Dedicata , vol.100 , pp. 157-171
    • Erschler, A.1
  • 49
    • 21644447856 scopus 로고    scopus 로고
    • Boundary behavior for groups of subexponential growth
    • [Ers04a] A. Erschler. Boundary behavior for groups of subexponential growth. Annals of Math., 160(3):1183–1210, 2004.
    • (2004) Annals of Math. , vol.160 , Issue.3 , pp. 1183-1210
    • Erschler, A.1
  • 50
    • 1642479002 scopus 로고    scopus 로고
    • Not residually finite groups of intermediate growth, commensurability and non-geometricity
    • [Ers04b] A. Erschler. Not residually finite groups of intermediate growth, commensurability and non-geometricity. J. Algebra, 272(1):154–172, 2004.
    • (2004) J. Algebra , vol.272 , Issue.1 , pp. 154-172
    • Erschler, A.1
  • 51
    • 66049152328 scopus 로고
    • Note on groups with and without full Banach mean value
    • [Føl57] E. Følner. Note on groups with and without full Banach mean value. Math. Scand., 5:5–11, 1957.
    • (1957) Math. Scand. , vol.5 , pp. 5-11
    • Følner, E.1
  • 52
    • 0030677012 scopus 로고    scopus 로고
    • On problems related to growth, entropy, and spectrum in group theory
    • [GdlH97] R. Grigorchuk and P. de la Harpe. On problems related to growth, entropy, and spectrum in group theory. J. Dynam. Control Systems, 3(1):51–89, 1997.
    • (1997) J. Dynam. Control Systems , vol.3 , Issue.1 , pp. 51-89
    • Grigorchuk, R.1    De La Harpe, P.2
  • 55
    • 0034311754 scopus 로고    scopus 로고
    • On a question of Atiyah. C. R. Acad. Sci. Paris S´r
    • On a question of Atiyah. C. R. Acad. Sci. Paris S´r. I Math., 331(9):663–668, 2000.
    • (2000) I Math. , vol.331 , Issue.9 , pp. 663-668
  • 56
    • 0001160004 scopus 로고    scopus 로고
    • Machì.` An example of an indexed language of intermediate growth. Theoret. Comput
    • [GM99] R. I. Grigorchuk and A. Machì.` An example of an indexed language of intermediate growth. Theoret. Comput. Sci., 215(1-2):325–327, 1999.
    • (1999) Sci. , vol.215 , Issue.1-2 , pp. 325-327
    • Grigorchuk, R.I.1
  • 58
    • 0039270229 scopus 로고    scopus 로고
    • Complete growth functions of hyperbolic groups
    • [GN97] R. I. Grigorchuk and T. Nagnibeda. Complete growth functions of hyperbolic groups. Invent. Math., 130(1):159–188, 1997.
    • (1997) Invent. Math. , vol.130 , Issue.1 , pp. 159-188
    • Grigorchuk, R.I.1    Nagnibeda, T.2
  • 60
    • 85027990980 scopus 로고
    • ´ Algebraic theory of automata. Akadémiai´ Kiad´o
    • [GP72] F. Gecseg and I. Peák.´ Algebraic theory of automata. Akadémiai´ Kiad´o, Budapest, 1972.
    • (1972) Budapest
    • Gecseg, F.1    Peák, I.2
  • 61
    • 0003872160 scopus 로고
    • Invariant means on topological groups and their applications
    • Van Nostrand Reinhold Co., New York
    • Invariant means on topological groups and their applications. Van Nostrand Mathematical Studies, No. 16. Van Nostrand Reinhold Co., New York, 1969.
    • (1969) Van Nostrand Mathematical Studies , vol.16
  • 62
    • 0002877634 scopus 로고
    • On Burnside’s problem on periodic groups
    • [Gri80] R. I. Grigorchuk. On Burnside’s problem on periodic groups. Funktsional. Anal. i Prilozhen., 14(1):53–54, 1980.
    • (1980) Funktsional. Anal. I Prilozhen. , vol.14 , Issue.1 , pp. 53-54
    • Grigorchuk, R.I.1
  • 63
    • 0002517311 scopus 로고
    • On the Milnor problem of group growth
    • [Gri83] R. I. Grigorchuk. On the Milnor problem of group growth. Dokl. Akad. Nauk SSSR, 271(1):30–33, 1983.
    • (1983) Dokl. Akad. Nauk SSSR , vol.271 , Issue.1 , pp. 30-33
    • Grigorchuk, R.I.1
  • 64
    • 0001109819 scopus 로고
    • Degrees of growth of finitely generated groups and the theory of invariant means
    • [Gri84a] R. I. Grigorchuk. Degrees of growth of finitely generated groups and the theory of invariant means. Izv. Akad. Nauk SSSR Ser. Mat., 48(5):939–985, 1984.
    • (1984) Izv. Akad. Nauk SSSR Ser. Mat. , vol.48 , Issue.5 , pp. 939-985
    • Grigorchuk, R.I.1
  • 65
    • 0043037653 scopus 로고
    • The construction of p-groups of intermediate growth having continuum factor groups
    • [Gri84b] R.I. Grigorchuk. The construction of p-groups of intermediate growth having continuum factor groups. Algebra i Logika, 23(4):383–394, 1984.
    • (1984) Algebra I Logika , vol.23 , Issue.4 , pp. 383-394
    • Grigorchuk, R.I.1
  • 66
    • 0347492233 scopus 로고
    • A relationship between algorithmic problems and entropy characteristics of groups
    • [Gri85] R. I. Grigorchuk. A relationship between algorithmic problems and entropy characteristics of groups. Dokl. Akad. Nauk SSSR, 284(1):24–29, 1985.
    • (1985) Dokl. Akad. Nauk SSSR , vol.284 , Issue.1 , pp. 24-29
    • Grigorchuk, R.I.1
  • 67
    • 85027965095 scopus 로고
    • I. Grigorchuk. Semigroups with cancellations of degree growth. Mat
    • I. Grigorchuk. Semigroups with cancellations of degree growth. Mat. Zametki, 43(3):305–319, 428, 1988.
    • (1988) Zametki, 43(3) , vol.428 , pp. 305-319
  • 68
    • 85027985161 scopus 로고
    • Growth and amenability of a semigroup and its group of quotients. In Proceedings of the International Symposium on the Semigroup Theory and its Related Fields
    • Shimane Univ
    • [Gri90] Growth and amenability of a semigroup and its group of quotients. In Proceedings of the International Symposium on the Semigroup Theory and its Related Fields (Kyoto, 1990), pages 103–108, Matsue, 1990. Shimane Univ.
    • (1990) Pages 103–108, Matsue, 1990
  • 69
    • 19444386961 scopus 로고    scopus 로고
    • Weight functions on groups, and criteria for the amenability of Beurling algebras
    • Weight functions on groups, and criteria for the amenability of Beurling algebras. Mat. Zametki, 60(3):370–382, 479, 1996.
    • (1996) Mat. Zametki, 60(3) , vol.479 , pp. 370-382
  • 70
    • 0002439178 scopus 로고    scopus 로고
    • An example of a finitely presented amenable group that does not belong to the class EG
    • [Gri98] R. I. Grigorchuk. An example of a finitely presented amenable group that does not belong to the class EG. Mat. Sb., 189(1):79–100, 1998.
    • (1998) Mat. Sb. , vol.189 , Issue.1 , pp. 79-100
    • Grigorchuk, R.I.1
  • 72
    • 33746269615 scopus 로고    scopus 로고
    • Branch groups
    • [Gri00a] R. I. Grigorchuk. Branch groups. Mat. Zametki, 67(6):852–858, 2000.
    • (2000) Mat. Zametki , vol.67 , Issue.6 , pp. 852-858
    • Grigorchuk, R.I.1
  • 73
    • 0002594622 scopus 로고    scopus 로고
    • Just infinite branch groups
    • Birkhäuser¨ Boston, Boston, MA
    • Just infinite branch groups. In New horizons in pro-p groups, volume 184 of Progr. Math., pages 121–179. Birkhäuser¨ Boston, Boston, MA, 2000.
    • (2000) New Horizons in Pro-P Groups, Volume 184 of Progr. Math. , pp. 121-179
  • 74
    • 51649160427 scopus 로고
    • Groups of polynomial growth and expanding maps
    • [Gro81] M. Gromov. Groups of polynomial growth and expanding maps. Publ. Math. IHES, 53:53–78, 1981.
    • (1981) Publ. Math. IHES , vol.53 , pp. 53-78
    • Gromov, M.1
  • 75
    • 0003195390 scopus 로고
    • Math. Sci. Res. Inst. Publ., pages 75–263. Springer, New York
    • [Gro87] M. Gromov. Hyperbolic groups. In Essays in group theory, volume 8 of Math. Sci. Res. Inst. Publ., pages 75–263. Springer, New York, 1987.
    • (1987) Hyperbolic Groups. in Essays in Group Theory , vol.8
    • Gromov, M.1
  • 77
    • 85028013062 scopus 로고    scopus 로고
    • Featured review on the paper “Non-amenable finitely presented torsion-by-cyclic groups” by Olshanskii, A. And Sapir, M. Publ
    • [GS02] R. Grigorchuk and Z. Sunik. Featured review on the paper “Non-amenable finitely presented torsion-by-cyclic groups” by Olshanskii, A. and Sapir, M. Publ. Math. Inst. Hautes E’tudes Sci. no. 96 (2002), 2002.
    • (2002) Math. Inst. Hautes E’tudes Sci.
    • Grigorchuk, R.1    Sunik, Z.2
  • 78
    • 12344320306 scopus 로고    scopus 로고
    • The group of automorphisms of a 3-generated 2-group of intermediate growth
    • [GS04] R. I. Grigorchuk and S. N. Sidki. The group of automorphisms of a 3-generated 2-group of intermediate growth. Internat. J. Algebra Comput., 14(5-6):667–676, 2004.
    • (2004) Internat. J. Algebra Comput. , vol.14 , Issue.5-6 , pp. 667-676
    • Grigorchuk, R.I.1    Sidki, S.N.2
  • 79
    • 0010960545 scopus 로고
    • On groups in which every element has finite order
    • [Gup89] N. Gupta. On groups in which every element has finite order. Amer. Math. Monthly, 96(4):297–308, 1989.
    • (1989) Amer. Math. Monthly , vol.96 , Issue.4 , pp. 297-308
    • Gupta, N.1
  • 80
    • 0346271600 scopus 로고    scopus 로고
    • London Math. Soc. (2), 68(3):671–682, 2003.
    • (2003) London Math. Soc. (2) , vol.68 , Issue.3 , pp. 671-682
  • 81
    • 0347756665 scopus 로고    scopus 로고
    • The uniqueness of the actions of certain branch groups on rooted trees
    • [GW03b] R. I. Grigorchuk and J. S. Wilson. The uniqueness of the actions of certain branch groups on rooted trees. Geom. Dedicata, 100:103–116, 2003.
    • (2003) Geom. Dedicata , vol.100 , pp. 103-116
    • Grigorchuk, R.I.1    Wilson, J.S.2
  • 82
    • 0026223216 scopus 로고
    • The complexity of Grigorchuk groups with application to cryptography. Theoret. Comput
    • [GZ91] Max Garzon and Yechezkel Zalcstein. The complexity of Grigorchuk groups with application to cryptography. Theoret. Comput. Sci., 88(1):83–98, 1991.
    • (1991) Sci. , vol.88 , Issue.1 , pp. 83-98
    • Garzon, M.1    Zalcstein, Y.2
  • 83
    • 1942463844 scopus 로고    scopus 로고
    • On the asymptotic spectrum of random walks on infinite families of graphs
    • Cambridge Univ. Press, Cambridge
    • On the asymptotic spectrum of random walks on infinite families of graphs. In Random walks and discrete potential theory (Cortona, 1997), Sympos. Math., XXXIX, pages 188–204. Cambridge Univ. Press, Cambridge, 1999.
    • (1999) Random Walks and Discrete Potential Theory (Cortona, 1997), Sympos. Math., XXXIX , pp. 188-204
  • 84
    • 0003231591 scopus 로고    scopus 로고
    • The lamplighter group as a group generated by a 2-state automaton, and its spectrum
    • [GŻ01] R. I. Grigorchuk and A. Żuk. The lamplighter group as a group generated by a 2-state automaton, and its spectrum. Geom. Dedicata, 87(1-3):209–244, 2001.
    • (2001) Geom. Dedicata , vol.87 , Issue.1-3 , pp. 209-244
    • Grigorchuk, R.I.1    Żuk, A.2
  • 85
    • 0036016737 scopus 로고    scopus 로고
    • On a torsion-free weakly branch group defined by a three state automaton
    • [GŻ02a] R. I. Grigorchuk and A. Żuk. On a torsion-free weakly branch group defined by a three state automaton. Internat. J. Algebra Comput., 12(1-2):223–246, 2002.
    • (2002) Internat. J. Algebra Comput. , vol.12 , Issue.1-2 , pp. 223-246
    • Grigorchuk, R.I.1    Żuk, A.2
  • 88
    • 33747130592 scopus 로고    scopus 로고
    • The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps
    • Walter de Gruyter GmbH & Co. KG, Berlin
    • The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps. In Random walks and geometry, pages 141–180. Walter de Gruyter GmbH & Co. KG, Berlin, 2004.
    • (2004) Random Walks and Geometry , pp. 141-180
  • 89
    • 33644691148 scopus 로고
    • Transformations defined by finite automata (In Russian)
    • J. Hoˇreiˇs. Transformations defined by finite automata (in Russian). Prob-lemy Kibernetiki, 9:23–26, 1963.
    • (1963) Prob-Lemy Kibernetiki , vol.9 , pp. 23-26
    • Hoˇreiˇs, J.1
  • 92
    • 0034911293 scopus 로고    scopus 로고
    • The growth function of context-free languages
    • [Inc01] R. Incitti. The growth function of context-free languages. Theoret. Comput. Sci., 255(1-2):601–605, 2001.
    • (2001) Theoret. Comput. Sci. , vol.255 , Issue.1-2 , pp. 601-605
    • Incitti, R.1
  • 93
    • 28444440402 scopus 로고    scopus 로고
    • “Münchhausen¨ trick” and amenability of self-similar groups
    • International Conference on Infinite Groups, Gaeta, 2003
    • [Kai] “Münchhausen¨ trick” and amenability of self-similar groups. To appear in IJAC (2005), special issue “International Conference on Infinite Groups, Gaeta, 2003”.
    • (2005) To Appear in IJAC
  • 95
    • 0040791308 scopus 로고
    • Kaloujnine. La structure des p-groupes de Sylow des groupes symétriques´ finis
    • Kaloujnine. La structure des p-groupes de Sylow des groupes symétriques´ finis. Ann. Sci. École Norm. Sup. (3), 65:239–276, 1948.
    • (1948) Ann. Sci. École Norm. Sup. (3) , vol.65 , pp. 239-276
  • 96
    • 0000742176 scopus 로고
    • “Problems in the theory of rings” revisited
    • [Kap70] I. Kaplansky. “Problems in the theory of rings” revisited. Amer. Math. Monthly, 77:445–454, 1970.
    • (1970) Amer. Math. Monthly , vol.77 , pp. 445-454
    • Kaplansky, I.1
  • 97
    • 0003589707 scopus 로고
    • Graduate Texts in Mathematics. Springer-Verlag, New York
    • [Kec95] A. S. Kechris. Classical descriptive set theory, volume 156 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995.
    • (1995) Classical Descriptive Set Theory , vol.156
    • Kechris, A.S.1
  • 98
    • 33847574798 scopus 로고
    • Symmetric random walks on groups
    • [Kes59] H. Kesten. Symmetric random walks on groups. Trans. Amer. Math. Soc., 92:336–354, 1959.
    • (1959) Trans. Amer. Math. Soc. , vol.92 , pp. 336-354
    • Kesten, H.1
  • 99
    • 0004117308 scopus 로고    scopus 로고
    • Universitext. Springer-Verlag, Berlin
    • [Kit98] B. P. Kitchens. Symbolic dynamics. Universitext. Springer-Verlag, Berlin, 1998.
    • (1998) Symbolic Dynamics
    • Kitchens, B.P.1
  • 101
    • 85027974733 scopus 로고    scopus 로고
    • The Kourovka notebook. Rossiĭskaya˘ Akademiya Nauk Sibirskoe Otdelenie Institut Matematiki
    • The Kourovka notebook. Rossiĭskaya˘ Akademiya Nauk Sibirskoe Otdelenie Institut Matematiki, Novosibirsk, 2002.
    • (2002) Novosibirsk
  • 103
    • 0007035881 scopus 로고    scopus 로고
    • The conjugacy problem in a class of 2-groups
    • [Leo98] Yu. G. Leonov. The conjugacy problem in a class of 2-groups. Mat. Zametki, 64(4):573–583, 1998.
    • (1998) Mat. Zametki , vol.64 , Issue.4 , pp. 573-583
    • Leonov, Y.G.1
  • 104
    • 84863972175 scopus 로고    scopus 로고
    • On a lower bound for the growth of a 3-generator 2-group
    • [Leo01] Yu. G. Leonov. On a lower bound for the growth of a 3-generator 2-group. Mat. Sb., 192(11):77–92, 2001.
    • (2001) Mat. Sb. , vol.192 , Issue.11 , pp. 77-92
    • Leonov, Y.G.1
  • 107
    • 0141676231 scopus 로고    scopus 로고
    • [LN02] Geom. Dedicata, 89:159–179, 2002.
    • (2002) Geom. Dedicata , vol.89 , pp. 159-179
  • 111
    • 33750361726 scopus 로고    scopus 로고
    • Birkhauser¨ Verlag, Basel
    • Progress in Mathematics. Birkhauser¨ Verlag, Basel, 2003.
    • (2003) Progress in Mathematics
  • 112
    • 35848964427 scopus 로고
    • Birkhauser¨ Verlag, Basel
    • Progress in Mathematics. Birkhauser¨ Verlag, Basel, 1994.
    • (1994) Progress in Mathematics
  • 114
    • 0003680739 scopus 로고    scopus 로고
    • An introduction to Kolmogorov complexity and its applications
    • Springer-Verlag, New York, second edition
    • [LV97] An introduction to Kolmogorov complexity and its applications. Graduate Texts in Computer Science. Springer-Verlag, New York, second edition, 1997.
    • (1997) Graduate Texts in Computer Science
  • 115
    • 85027999477 scopus 로고
    • G. Lysënok.¨ A set of defining relations for the Grigorchuk group. Mat
    • G. Lysënok.¨ A set of defining relations for the Grigorchuk group. Mat. Zametki, 38(4):503–516, 634, 1985.
    • (1985) Zametki, 38(4) , vol.634 , pp. 503-516
  • 116
    • 0002158117 scopus 로고
    • Finite factor groups of the unimodular group
    • Finite factor groups of the unimodular group. Ann. of Math. (2), 81:31–37, 1965.
    • (1965) Ann. of Math. (2) , vol.81 , pp. 31-37
  • 117
    • 0000362660 scopus 로고
    • Problem 5603
    • [Mil68] J. Milnor. Problem 5603. Amer. Math. Monthly, 75:685–686, 1968.
    • (1968) Amer. Math. Monthly , vol.75 , pp. 685-686
    • Milnor, J.1
  • 118
    • 0035585256 scopus 로고    scopus 로고
    • On growth of Grigorchuk groups. Internat
    • [MP01] Roman Muchnik and Igor Pak. On growth of Grigorchuk groups. Internat. J. Algebra Comput., 11(1):1–17, 2001.
    • (2001) J. Algebra Comput. , vol.11 , Issue.1 , pp. 1-17
    • Muchnik, R.1    Pak, I.2
  • 119
    • 0030519655 scopus 로고    scopus 로고
    • Fundamental group and contractible closed geodesics
    • [Nab96] A. Nabutovsky. Fundamental group and contractible closed geodesics. Comm. Pure Appl. Math., 49(12):1257–1270, 1996.
    • (1996) Comm. Pure Appl. Math. , vol.49 , Issue.12 , pp. 1257-1270
    • Nabutovsky, A.1
  • 121
    • 15744383940 scopus 로고    scopus 로고
    • Cuntz-Pimsner algebras of group actions
    • [Nek04] V. V. Nekrashevych. Cuntz-Pimsner algebras of group actions. J. Operator Theory, 52(2):223–249, 2004.
    • (2004) J. Operator Theory , vol.52 , Issue.2 , pp. 223-249
    • Nekrashevych, V.V.1
  • 123
    • 0009916426 scopus 로고
    • ′ˇsanski˘ı. On the question of the existence of an invariant mean on a group. Uspekhi Mat
    • ′ˇsanski˘ı. On the question of the existence of an invariant mean on a group. Uspekhi Mat. Nauk, 35(4(214)):199–200, 1980.
    • (1980) Nauk, 35(4(214)) , pp. 199-200
  • 125
    • 0004226607 scopus 로고
    • Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI
    • [Pat88] A. L. T. Paterson. Amenability, volume 29 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1988.
    • (1988) Amenability , vol.29
    • Paterson, A.L.T.1
  • 126
    • 0346225307 scopus 로고    scopus 로고
    • L. Pervova. Everywhere dense subgroups of a group of tree automorphisms. Tr. Mat. Inst
    • L. Pervova. Everywhere dense subgroups of a group of tree automorphisms. Tr. Mat. Inst. Steklova, 231:356–367, 2000.
    • (2000) Steklova , vol.231 , pp. 356-367
  • 127
    • 33847621615 scopus 로고    scopus 로고
    • The congruence property of AT-groups
    • The congruence property of AT-groups. Algebra Logika, 41(5):553–567, 634, 2002.
    • (2002) Algebra Logika, 41(5) , vol.634 , pp. 553-567
  • 129
    • 85027998531 scopus 로고    scopus 로고
    • Maximal subgroups of non locally finite fractal groups
    • J. of Alg. and Comput
    • [Per05] Maximal subgroups of non locally finite fractal groups., 2005. To appear in Inter. J. of Alg. and Comput.
    • (2005) To Appear in Inter
  • 130
    • 0043187213 scopus 로고    scopus 로고
    • Dessins d’enfants and Hubbard trees. Ann. Sci
    • Dessins d’enfants and Hubbard trees. Ann. Sci. École Norm. Sup. (4), 33(5):671–693, 2000.
    • (2000) École Norm. Sup. (4) , vol.33 , Issue.5 , pp. 671-693
  • 131
    • 84972581034 scopus 로고
    • Simplicity of the C -algebra associated with the free group on two generators
    • ∗ -algebra associated with the free group on two generators. Duke Math. J., 42:151–156, 1975.
    • (1975) Duke Math. J. , vol.42 , pp. 151-156
    • Powers, R.T.1
  • 134
    • 0141694439 scopus 로고
    • Centralizers of elements in a group of tree automorphisms
    • [Roz93] A. V. Rozhkov. Centralizers of elements in a group of tree automorphisms. Izv. Ross. Akad. Nauk Ser. Mat., 57(6):82–105, 1993.
    • (1993) Izv. Ross. Akad. Nauk Ser. Mat. , vol.57 , Issue.6 , pp. 82-105
    • Rozhkov, A.V.1
  • 135
    • 66049118059 scopus 로고    scopus 로고
    • The conjugacy problem in an automorphism group of an infinite tree
    • [Roz98] A. V. Rozhkov. The conjugacy problem in an automorphism group of an infinite tree. Mat. Zametki, 64(4):592–597, 1998.
    • (1998) Mat. Zametki , vol.64 , Issue.4 , pp. 592-597
    • Rozhkov, A.V.1
  • 136
  • 137
    • 31044433265 scopus 로고    scopus 로고
    • Mat. Zametki, 72(1):102–117, 2002.
    • (2002) Mat. Zametki , vol.72 , Issue.1 , pp. 102-117
  • 138
    • 0002291626 scopus 로고
    • On the profinite topology on a free group
    • [RZ93] L. Ribes and P. A. Zalesskii. On the profinite topology on a free group. Bull. London Math. Soc., 25(1):37–43, 1993.
    • (1993) Bull. London Math. Soc. , vol.25 , Issue.1 , pp. 37-43
    • Ribes, L.1    Zalesskii, P.A.2
  • 141
    • 0034349067 scopus 로고    scopus 로고
    • Rigidity of commensurators and irreducible lattices
    • [Sha00] Y. Shalom. Rigidity of commensurators and irreducible lattices. Invent. Math., 141(1):1–54, 2000.
    • (2000) Invent. Math. , vol.141 , Issue.1 , pp. 1-54
    • Shalom, Y.1
  • 142
    • 0010957318 scopus 로고
    • On a 2-generated infinite 3-group: Subgroups and automorphisms
    • [Sid87a] S. Sidki. On a 2-generated infinite 3-group: subgroups and automorphisms. J. Algebra, 110(1):24–55, 1987.
    • (1987) J. Algebra , vol.110 , Issue.1 , pp. 24-55
    • Sidki, S.1
  • 143
    • 0002782677 scopus 로고
    • On a 2-generated infinite 3-group: The presentation problem
    • [Sid87b] S. Sidki. On a 2-generated infinite 3-group: the presentation problem. J. Algebra, 110(1):13–23, 1987.
    • (1987) J. Algebra , vol.110 , Issue.1 , pp. 13-23
    • Sidki, S.1
  • 144
    • 0038869924 scopus 로고    scopus 로고
    • Sidki. A primitive ring associated to a Burnside 3-group
    • Sidki. A primitive ring associated to a Burnside 3-group. J. London Math. Soc. (2), 55(1):55–64, 1997.
    • (1997) J. London Math. Soc. (2) , vol.55 , Issue.1 , pp. 55-64
  • 145
    • 85027981513 scopus 로고    scopus 로고
    • Instituto de Matemática´ Pura e Aplicada (IMPA)
    • Instituto de Matemática´ Pura e Aplicada (IMPA), Rio de Janeiro, 1998.
    • (1998) Rio De Janeiro
  • 146
    • 10044284507 scopus 로고    scopus 로고
    • Finite automata of polynomial growth do not generate a free group
    • [Sid04] S. Sidki. Finite automata of polynomial growth do not generate a free group. Geom. Dedicata, 108:193–204, 2004.
    • (2004) Geom. Dedicata , vol.108 , pp. 193-204
    • Sidki, S.1
  • 148
    • 85027982878 scopus 로고    scopus 로고
    • Hausdorff dimension of branched automaton groups, 2005
    • [Sun05] Z. Sunik. Hausdorff dimension of branched automaton groups, 2005. Preprint.
    • Preprint.
    • Sunik, Z.1
  • 149
    • 0042414127 scopus 로고    scopus 로고
    • Free subgroups of branch groups. Arch
    • [SW03] Free subgroups of branch groups. Arch. Math. (Basel), 80(5):458–463, 2003.
    • (2003) Math. (Basel) , vol.80 , Issue.5 , pp. 458-463
  • 150
    • 0003705593 scopus 로고    scopus 로고
    • London Mathematical Society Student Texts. Cambridge University Press, Cambridge
    • [Ter99] A. Terras. Fourier analysis on finite groups and applications, volume 43 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1999.
    • (1999) Fourier Analysis on Finite Groups and Applications , vol.43
    • Terras, A.1
  • 151
    • 0013199326 scopus 로고
    • Eine Charakterisierung diskreter Gruppen vom Typ I
    • [Tho68] E. Thoma. Eine Charakterisierung diskreter Gruppen vom Typ I. Invent. Math., 6:190–196, 1968.
    • (1968) Invent. Math. , vol.6 , pp. 190-196
    • Thoma, E.1
  • 152
    • 0041081036 scopus 로고
    • Amenability and approximation of infinite groups
    • [Ver82] A. Vershik. Amenability and approximation of infinite groups. Selecta Math. Soviet., 2(4):311–330, 1982.
    • (1982) Selecta Math. Soviet. , vol.2 , Issue.4 , pp. 311-330
    • Vershik, A.1
  • 154
    • 85028017743 scopus 로고    scopus 로고
    • Infinite torsion groups arising as generalizations of the second Grigorchuk group
    • Infinite torsion groups arising as generalizations of the second Grigorchuk group. In Algebra (Moscow, 1998), pages 357–377. de Gruyter, Berlin, 2000.
    • (2000) Algebra (Moscow, 1998), Pages 357–377. De Gruyter, Berlin
  • 156
    • 0004111784 scopus 로고
    • Cambridge University Press, Cambridge
    • [Wag93] S. Wagon. The Banach-Tarski paradox. Cambridge University Press, Cambridge, 1993.
    • (1993) The Banach-Tarski Paradox
    • Wagon, S.1
  • 157
    • 0001959952 scopus 로고
    • Zel’manov. Solution of the restricted burnside problem for groups of odd exponent
    • Zel’manov. Solution of the restricted burnside problem for groups of odd exponent. Izv. Akad. Nauk SSSR, Ser. Mat., 54(1):42–59, 1990.
    • (1990) Izv. Akad. Nauk SSSR, Ser. Mat. , vol.54 , Issue.1 , pp. 42-59
  • 158
    • 0000023688 scopus 로고
    • Manov. Solution of the restricted burnside problem for 2-groups
    • [Zel91] E.I. Zel’manov. Solution of the restricted burnside problem for 2-groups. Mat. Sb., 182(4):568–592, 1991.
    • (1991) Mat. Sb. , vol.182 , Issue.4 , pp. 568-592
    • Zel, E.I.1


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