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Algebra Discrete Math., 2003, Issue 4, Pages 21–32 (Mi adm390)  

This article is cited in 11 scientific papers (total in 11 papers)

RESEARCH ARTICLE

Post-critically finite self-similar groups

E. Bondarenko, V. Nekrashevycha

a Kyiv Taras Shevchenko University Mechanics and Mathematics Faculty Algebra Department Volodymyrska, 60,  Kyiv, Ukraine, 01033

Abstract: We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting.

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Citation: E. Bondarenko, V. Nekrashevych, “Post-critically finite self-similar groups”, Algebra Discrete Math., 2003, no. 4, 21–32

Citation in format AMSBIB
\Bibitem{BonNek03}
\by E.~Bondarenko, V.~Nekrashevych
\paper Post-critically finite self-similar groups
\jour Algebra Discrete Math.
\yr 2003
\issue 4
\pages 21--32
\mathnet{http://mi.mathnet.ru/adm390}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2070400}
\zmath{https://zbmath.org/?q=an:1068.20028}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Holt D.F., Roever C.E., “Groups with Indexed Co-Word Problem”, Int. J. Algebr. Comput., 16:5 (2006), 985–1014  crossref  mathscinet  zmath  isi  scopus
    2. Nekrashevych V., Teplyaev A., “Groups and Analysis on Fractals”, Analysis on Graphs and its Applications, Proceedings of Symposia in Pure Mathematics, 77, eds. Exner P., Keating J., Kuchment P., Sunada T., Teplyaev A., 2008, 143–180  crossref  mathscinet  zmath  isi
    3. Bartholdi L., Nekrashevych V.V., “Iterated Monodromy Groups of Quadratic Polynomials, I”, Group. Geom. Dyn., 2:3 (2008), 309–336  crossref  mathscinet  zmath  isi
    4. Kaimanovich V.A., “Self-Similarity and Random Walks”, Nanowires - Synthesis, Properties, Assembly and Applications, Materials Research Society Symposium Proceedings, 1144, eds. Cui Y., Lauhon L., Talin A., Bakkers E., 2009, 45–70  mathscinet  isi
    5. Bartholdi L., Kaimanovich V.A., Nekrashevych V.V., “Amenability of Automata Groups”, Duke Math. J., 154:3 (2010), 575–598  crossref  mathscinet  zmath  isi  elib  scopus
    6. D'Angeli D., Donno A., Matter M., Nagnibeda T., “Schreier Graphs of the Basilica Group”, J. Mod. Dyn., 4:1 (2010), 167–205  crossref  mathscinet  zmath  isi  scopus
    7. Makisumi Sh., Stadnyk G., Steinhurst B., “Modified Hanoi Towers Groups and Limit Spaces”, Int. J. Algebr. Comput., 21:6 (2011), 867–887  crossref  mathscinet  zmath  isi  scopus
    8. Kelleher D.J., Steinhurst B.A., Wong Ch.-M.M., “From Self-Similar Structures to Self-Similar Groups”, Int. J. Algebr. Comput., 22:7 (2012), 1250056  crossref  mathscinet  zmath  isi  elib  scopus
    9. Bondarenko I.V., “Growth of Schreier Graphs of Automaton Groups”, Math. Ann., 354:2 (2012), 765–785  crossref  mathscinet  zmath  isi  elib  scopus
    10. Jones R., “Fixed-Point-Free Elements of Iterated Monodromy Groups”, Trans. Am. Math. Soc., 367:3 (2015), PII S0002-9947(2014)06347-2, 2023–2049  crossref  mathscinet  zmath  isi
    11. Bondarenko I., D'Angeli D., Nagnibeda T., “Ends of Schreier Graphs and Cut-Points of Limit Spaces of Self-Similar Groups”, J. Fractal Geom., 4:4 (2017), 369–424  crossref  mathscinet  zmath  isi
  • Algebra and Discrete Mathematics
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