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Mat. Sb., 1998, Volume 189, Number 1, Pages 79–100 (Mi msb293)  

This article is cited in 51 scientific papers (total in 51 papers)

An example of a finitely presented amenable group not belonging to the class $EG$

R. I. Grigorchuk

Abstract: An example of a finitely presented amenable group not belonging to the class $EG$ of elementary amenable groups is constructed. By this means, a solution of the Day problem in the class of finitely presented groups is given.


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English version:
Sbornik: Mathematics, 1998, 189:1, 75–95

Bibliographic databases:

UDC: 512
MSC: 20F05, 43A07
Received: 30.12.1996

Citation: R. I. Grigorchuk, “An example of a finitely presented amenable group not belonging to the class $EG$”, Mat. Sb., 189:1 (1998), 79–100; Sb. Math., 189:1 (1998), 75–95

Citation in format AMSBIB
\by R.~I.~Grigorchuk
\paper An example of a~finitely presented amenable group not belonging to the~class~$EG$
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 1
\pages 79--100
\jour Sb. Math.
\yr 1998
\vol 189
\issue 1
\pages 75--95

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    This publication is cited in the following articles:
    1. P. de la Harpe, R. I. Grigorchuk, T. Ceccherini-Silberstein, “Amenability and Paradoxical Decompositions for Pseudogroups and for Discrete Metric Spaces”, Proc. Steklov Inst. Math., 224 (1999), 57–97  mathnet  mathscinet  zmath
    2. Yu. G. Leonov, “On a lower bound for the growth function of the Grigorchuk group”, Math. Notes, 67:3 (2000), 403–405  mathnet  crossref  crossref  mathscinet  zmath
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    4. Yu. G. Leonov, “A lower bound for the growth of a 3-generator 2-group”, Sb. Math., 192:11 (2001), 1661–1676  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Ol'Shanskii A.Yu., Sapir M.V., “Non-amenable finitely presented torsion-by-cyclic groups”, Electron. Res. Announc. Amer. Math. Soc., 7 (2001), 63–71  crossref  mathscinet  isi  scopus  scopus  scopus
    6. Röver C.E., “Abstract commensurators of groups acting on rooted trees”, Geom. Dedicata, 94:1 (2002), 45–61  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. Grigorchuk R.I., Żuk A., “On a torsion-free weakly branch group defined by a three state automaton”, Internat. J. Algebra Comput., 12:1-2 (2002), 223–246  crossref  mathscinet  zmath  isi  elib
    8. Sapir M., Wise D.T., “Ascending HNN extensions of residually finite groups can be non-Hopfian and can have very few finite quotients”, J. Pure Appl. Algebra, 166:1-2 (2002), 191–202  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Bartholdi L., “Endomorphic presentations of branch groups”, J. Algebra, 268:2 (2003), 419–443  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    10. Ol'Shanskii A.Yu., Sapir M.V., “Non-amenable finitely presented torsion-by-cyclic groups”, Publ. Math. Inst. Hautes Études Sci., 2003, no. 96, 43–169  crossref  mathscinet  isi
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    12. Navas A.S., “Quelques groupes moyennables de difféomorphismes de l'intervalle [Some amenable groups of diffeomorphisms of the interval]”, Bol. Soc. Mat. Mexicana (3), 10:2 (2004), 219–244  mathscinet  isi
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    14. Navas A., “Groupes résolubles de difféomorphismes de l'intervalle, du cercle et de la droite [Solvable groups of diffeomorphisms of the interval, the circle and the real line]”, Bull. Braz. Math. Soc. (N.S.), 35:1 (2004), 13–50  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. J. Math. Sci. (N. Y.), 140:3 (2007), 391–397  mathnet  crossref  mathscinet  zmath  elib
    16. Bartholdi L., Virág B., “Amenability via random walks”, Duke Math. J., 130:1 (2005), 39–56  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. Brin M.G., “Elementary amenable subgroups of R. Thompson's group $F$”, Internat. J. Algebra Comput., 15:4 (2005), 619–642  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
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    19. Nekrashevych V., “Self-similar inverse semigroups and Smale spaces”, Internat. J. Algebra Comput., 16:5 (2006), 849–874  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    20. Smith J., “The asymptotic dimension of the first Grigorchuk group is infinity”, Rev. Mat. Complut., 20:1 (2007), 119–121  crossref  mathscinet  zmath  isi
    21. Grigorchuk R., Nekrashevych V., “Self-similar groups, operator algebras and Schur complement”, J. Mod. Dyn., 1:3 (2007), 323–370  crossref  mathscinet  zmath  isi
    22. de Cornulier Y., Guyot L., Pitsch W., “On the isolated points in the space of groups”, J. Algebra, 307:1 (2007), 254–277  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    23. Burillo J., Cleary S., Wiest B., “Computational explorations in Thompson's group F”, Geometric Group Theory, Trends in Mathematics, 2007, 21–35  crossref  mathscinet  zmath  isi
    24. Grigorchuk R., Savchuk D., Sunic Z., “The spectral problem, substitutions and iterated monodromy”, Probability and Mathematical Physics: A Volume in Honor of Stanislav Molchanov, Crm Proceedings & Lecture Notes, 42, 2007, 225–248  crossref  mathscinet  zmath  isi
    25. Farley D., “The action of Thompson's group on a CAT(0) boundary”, Groups Geom. Dyn., 2:2 (2008), 185–222  crossref  mathscinet  zmath  isi
    26. Delzant T., Grigorchuk R., “Homomorphic images of branch groups, and Serre's property (FA)”, In Memory of Alexander Reznikov, Progress in Mathematics, 265, 2008, 353–375  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    27. V. S. Atabekyan, A. S. Pailevanyan, “Vlozhenie absolyutno svobodnykh grupp v gruppy $B(m,n,1)$”, Uch. zapiski EGU, ser. Fizika i Matematika, 2008, no. 3, 25–33  mathnet
    28. Brieussel J., “Amenability and non-uniform growth of some directed automorphism groups of a rooted tree”, Math. Z., 263:2 (2009), 265–293  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    29. Grigorchuk R.I., Ivanov S.V., “On Dehn functions of infinite presentations of groups”, Geom. Funct. Anal., 18:6 (2009), 1841–1874  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    30. Kaimanovich V.A., “Self-similarity and Random Walks”, Nanowires - Synthesis, Properties, Assembly and Applications, Materials Research Society Symposium Proceedings, 1144, 2009, 45–70  mathscinet  isi
    31. Bartholdi L., Kaimanovich V.A., Nekrashevych V.V., “Amenability of Automata Groups”, Duke Mathematical Journal, 154:3 (2010), 575–598  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
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    34. R. I. Grigorchuk, “Some topics in the dynamics of group actions on rooted trees”, Proc. Steklov Inst. Math., 273 (2011), 64–175  mathnet  crossref  mathscinet  zmath  isi  elib
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    36. Haagerup U., Picioroaga G., “New Presentations of Thompson's Groups and Applications”, Journal of Operator Theory, 66:1 (2011), 217–232  mathscinet  zmath  isi
    37. Savchuk D., Vorobets Ya., “Automata generating free products of groups of order 2”, J Algebra, 336:1 (2011), 53–66  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    38. Benli M.G., “Profinite Completion of Grigorchuk's Group Is Not Finitely Presented”, Int. J. Algebr. Comput., 22:5 (2012), 1250045  crossref  mathscinet  zmath  isi
    39. Benli M.G., “Indicable Groups and Endomorphic Presentations”, Glasg. Math. J., 54:2 (2012), 335–344  crossref  mathscinet  zmath  isi  elib  scopus
    40. Gandini G., “Cohomological Invariants and the Classifying Space for Proper Actions”, Group. Geom. Dyn., 6:4 (2012), 659–675  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    41. Bartholdi L., “(Self-)Similar Groups and the Farrell-Jones Conjectures”, Group. Geom. Dyn., 7:1 (2013), 1–11  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    42. Hartung R., “Algorithms for Finitely l-Presented Groups and their Applications to Some Self-Similar Groups”, Expo. Math., 31:4 (2013), 368–384  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
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    44. Grigorchuk R., “On the Gap Conjecture Concerning Group Growth”, Bull. Math. Sci., 4:1 (2014), 113–128  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    45. L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Russian Math. Surveys, 70:2 (2015), 203–248  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    46. Grigorchuk R., Leonov Y., Nekrashevych V., Sushchansky V., “Self-similar groups, automatic sequences, and unitriangular representations”, Bull. Math. Sci., 6:2 (2016), 231–285  crossref  mathscinet  zmath  isi  scopus
    47. Mihalik M.L., “Semistability and simple connectivity at of finitely generated groups with a finite series of commensurated subgroups”, Algebr. Geom. Topol., 16:6 (2016), 3615–3640  crossref  mathscinet  zmath  isi  scopus
    48. Yamauchi T., “Hereditarily infinite-dimensional property for asymptotic dimension and graphs with large girth”, Fundam. Math., 236:2 (2017), 187–192  crossref  mathscinet  zmath  isi  scopus
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    50. Holt D. Rees S. Rover C., “Groups, Languages and Automata”, Groups, Languages and Automata, London Mathematical Society Student Texts, 88, Cambridge Univ Press, 2017, 1–294  crossref  mathscinet  zmath  isi
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