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Tr. Mat. Inst. Steklova, 2000, Volume 231, Pages 356–367 (Mi tm523)  

This article is cited in 15 scientific papers (total in 15 papers)

Everywhere Dense Subgroups of One Group of Tree Automorphisms

E. L. Pervova

Chelyabinsk State University

Abstract: The well-known question of the existence, in the Grigorchuk 2-groups, of subgroups that are everywhere dense in the profinite topology is answered negatively. This is shown to be equivalent to the fact that these groups do not contain maximal subgroups of infinite index.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 231, 339–350

Bibliographic databases:
UDC: 512.54
Received in February 2000

Citation: E. L. Pervova, “Everywhere Dense Subgroups of One Group of Tree Automorphisms”, Dynamical systems, automata, and infinite groups, Collected papers, Tr. Mat. Inst. Steklova, 231, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 356–367; Proc. Steklov Inst. Math., 231 (2000), 339–350

Citation in format AMSBIB
\Bibitem{Per00}
\by E.~L.~Pervova
\paper Everywhere Dense Subgroups of One Group of Tree Automorphisms
\inbook Dynamical systems, automata, and infinite groups
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 231
\pages 356--367
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm523}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1841763}
\zmath{https://zbmath.org/?q=an:1018.20019}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 231
\pages 339--350


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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. Grigorchuk R.I., Wilson J.S., “On finitely generated subgroups of a certain periodic group”, Doklady Mathematics, 65:3 (2002), 404–404  zmath  isi
    2. Grigorchuk R.I., Wilson J.S., “A structural property concerning abstract commensurability of subgroups”, Journal of the London Mathematical Society–Second Series, 68:3 (2003), 671–682  crossref  mathscinet  zmath  isi  scopus  scopus
    3. de Cornulier Y., “Finitely presented wreath products and double coset decompositions”, Geometriae Dedicata, 122:1 (2006), 89–108  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Gelander Ts., Glasner Ya., “Countable primitive groups”, Geometric and Functional Analysis, 17:5 (2007), 1479–1523  crossref  mathscinet  zmath  isi  scopus  scopus
    5. 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
    6. Hartung R., “Coset Enumeration for Certain Infinitely Presented Groups”, Internat J Algebra Comput, 21:8 (2011), 1369–1380  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Malyshev A. Pak I., “Growth in Product Replacement Graphs of Grigorchuk Groups”, J. Group Theory, 18:2 (2015), 209–234  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Kantor W.M., Lubotzky A., Shalev A., “Invariable Generation of Infinite Groups”, J. Algebra, 421:SI (2015), 296–310  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Mustafa Gökhan Benli, Rostislav Grigorchuk, “Uncountably many $2$-generated just-infinite branch pro-2 groups”, Algebra Discrete Math., 19:1 (2015), 8–18  mathnet  mathscinet
    10. Bartholdi L., Erschler A., “Ordering the space of finitely generated groups”, Ann. Inst. Fourier, 65:5 (2015), 2091–2144  crossref  mathscinet  zmath  isi  elib  scopus
    11. Myropolska A., “Andrews-Curtis and Nielsen Equivalence Relations on Some Infinite Groups”, J. Group Theory, 19:1 (2016), 161–178  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Bou-Rabee Kh. Leemann P.-H. Nagnibeda T., “Weakly maximal subgroups in regular branch groups”, J. Algebra, 455 (2016), 347–357  crossref  mathscinet  zmath  isi  elib  scopus
    13. Garrido A., “Abstract commensurability and the Gupta–Sidki group”, Group. Geom. Dyn., 10:2 (2016), 523–543  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    14. Alexoudas T., Klopsch B., Thillaisundaram A., “Maximal subgroups of multi-edge spinal groups”, Group. Geom. Dyn., 10:2 (2016), 619–648  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. Myropolska A., “Nielsen Equivalence in Gupta-Sidki Groups”, Proc. Amer. Math. Soc., 145:8 (2017), 3331–3342  crossref  mathscinet  zmath  isi  scopus  scopus
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