Groupes engendrés par les automates

Żuk, Andrzej

Séminaire Bourbaki - Volume 2006/2007 - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 971, 34 p.

Zbl

@incollection{AST_2008__317__141_0,
     author = {\.Zuk, Andrzej},
     title = {Groupes engendr\'es par les automates},
     booktitle = {S\'eminaire Bourbaki - Volume 2006/2007  - Expos\'es 967-981},
     series = {Ast\'erisque},
     note = {talk:971},
     pages = {141--174},
     year = {2008},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {317},
     zbl = {1278.20047},
     language = {fr},
     url = {https://www.numdam.org/item/AST_2008__317__141_0/}
}

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Żuk, Andrzej. Groupes engendrés par les automates, dans Séminaire Bourbaki - Volume 2006/2007  - Exposés 967-981, Astérisque, no. 317 (2008), Exposé no. 971, 34 p.. https://www.numdam.org/item/AST_2008__317__141_0/

Bibliographie
Cité par

[1] S. V. Alešin - Finite automata and the Burnside problem for periodic groups, Mat. Zametki 11 (1972), p. 319-328. | Zbl

[2] M. F. Atiyah - Elliptic operators, discrete groups and von Neumann algebras, in Colloque "Analyse et Topologie" en l'honneur de Henri Cartan (Orsay, 1974), Soc. Math. France, 1976, p. 43-72. Astérisque, No. 32-33. | Zbl | Numdam

[3] L. Bartholdi & B. Virág - Amenability via random walks, Duke Math. J. 130 (2005), p. 39-56. | Zbl | DOI

[4] E. Breuillard & T. Gelander - Cheeger constant and algebraic entropy of linear groups, International Mathematical Research Notices 56 (2005), p. 3511-3523. | Zbl | DOI

[5] J. Brieussel - Croissance et moyennabilité de certains groupes d'automorphismes d'un arbre enraciné, Thèse, Université Paris 7, 2008.

[6] M. M. Day - Amenable semigroups, Illinois J. Math. 1 (1957), p. 509-544. | Zbl

[7]W. Dicks & T. Schick - The spectral measure of certain elements of the complex group ring of a wreath product, Geom. Dedicata 93 (2002), p. 121-137. | Zbl | DOI

[8] A. Eskin, S. Mozes & H. Oh - On uniform exponential growth for linear groups, Invent. Math. 160 (2005), p. 1-30. | Zbl | DOI

[9] J. Fabrykowski & N. Gupta - On groups with sub-exponential growth functions, J. Indian Math. Soc. (N.S.) 49 (1985), p. 249-256 | Zbl

J. Fabrykowski & N. Gupta - On groups with sub-exponential growth functions, J. Indian Math. Soc. (N.S.) 49, p. 249-256 (1985). | Zbl

[10] J. Fabrykowski & N. Gupta, On groups with sub-exponential growth functions. II, J. Indian Math. Soc. (N.S.) 56 (1991), p. 217-228. | Zbl

[11] F. Gecseg & I. Peák - Algebraic theory of automata, Akadémiai Kiadó, 1972, Disquisitiones Mathematicae Hungaricae, 2. | Zbl

[12] Y. Glasner & S. Mozes - Automata and square complexes, Geom. Dedicata 111 (2005), p. 43-64. | Zbl | DOI

[13] R. Grigorchuk - Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), p. 939-985. | Zbl

[14] R. Grigorchuk, P. Linnell, T. Schick & A. Żuk - On a question of Atiyah, C. R. Acad. Sci. Paris Sér. I Math. 331 (2000), p. 663-668. | Zbl | DOI

[15] R. Grigorchuk & A. Żuk - The lamplighter group as a group generated by a $2$ -state automaton, and its spectrum, Geom. Dedicata 87 (2001), p. 209-244. | Zbl | DOI

[16] R. Grigorchuk & A. Żuk, On a torsion-free weakly branch group defined by a three state automaton, Internat. J. Algebra Comput. 12 (2002), p. 223-246, International Conférence on Géométrie and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000). | Zbl | DOI

[17] R. Grigorchuk & A. Żuk, Spectral properties of a torsion-free weakly branch group defined by a three state automaton, in Computational and statistical group theory (Las Vegas, NV/Hoboken, NJ, 2001), Contemp. Math., vol. 298, Amer. Math. Soc., 2002, p. 57-82. | Zbl | DOI

[18] M. Gromov - Structures métriques pour les variétés riemanniennes, Textes Mathématiques, vol. 1, CEDIC, 1981, Edited by J. Lafontaine and P. Pansu. | Zbl

[19] M. Gromov, Hyperbolic groups, in Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, 1987, p. 75-263. | Zbl | DOI

[20] N. Gupta & S. Sidki - Some infinite $p$ -groups, Algebra i Logika 22 (1983), p. 584-589. | Zbl | EuDML | DOI

[21] H. Kesten - Full Banach mean values on countable groups, Math. Scand. 7 (1959), p. 146-156. | Zbl | EuDML | DOI

[22] V. B. Kudryavtsev, S. V. Aleshin & A. S. Podkolzin - Beedehue e meopuιo aemomamoe (Introduction to automata theory), "Nauka", 1985. | Zbl

[23] W. Lück - $L^{2}$ -invariants : theory and applications to geometry and $K$ -theory, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 44, Springer, 2002. | Zbl

[24] G. A. Margulis - Discrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 17, Springer, 1991. | Zbl

[25] J. Milnor - Problems and Solutions : Advanced Problems : 5600-5609, Amer. Math. Monthly 75 (1968), p. 685-687. | DOI

[26] V. Nekrashevych - Self-similar groups, Mathematical Surveys and Monographs, vol. 117, American Mathematical Society, 2005. | Zbl | DOI

[27] J. Von Neumann - Zur allgemeinen Theorie des Maßes, Fundamenta Mathematica 13 (1929), p. 73-116. | JFM | EuDML | DOI

[28] P. S. Novikov & S. I. Adjan - Infinite periodic groups. I, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), p. 212-244, 251-524, 709-731. | Zbl

[29] J.-F. Planchat - Groupe d'Aleshin, mémoire de DEA, Paris VII, 2005.

[30] J-P. Serre - Arbres, amalgames, $S L_{2}$ , Société Mathématique de France, 1977, Astérisque, No. 46. | Zbl | Numdam

[31] V. Ī. Susčans'Kiĭ - Periodic $p$ -groups of permutations and the unrestricted Burnside problem, Dokl. Akad. Nauk SSSR 247 (1979), p. 557-561. | Zbl

[32] B. Virag - Self-similar walk on a self-similar group, prépublication, 2003.

[33] J. S. Wilson - On exponential growth and uniformly exponential growth for groups, Invent. Math. 155 (2004), p. 287-303. | Zbl | DOI

[34] A. Żuk - Automata groups, livre à paraître. | Zbl