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Zapiski Nauchnykh Seminarov POMI, 2005, Volume 326, Pages 85–96 (Mi znsl339)  
This article is cited in 11 scientific papers (total in 11 papers)

Amenable actions of nonamenable groups

R. I. Grigorchuk, V. V. Nekrashevych

Texas A&M University
Full-text PDF (204 kB) Citations (11)
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Abstract: We give two ways of constructing amenable (in the sense of Greenleaf) actions of nonamenable groups. In the first part of the paper we construct a class of faithful transitive amenable actions of the free group using Schreier graphs. In the second part we show that every finitely generated residually finite group can be embedded into a bigger residually finite group, which acts level-transitively on a locally finite rooted tree, so that the induced action on the boundary of the tree is amenable on every orbit.
Received: 26.05.2005
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 140, Issue 3, Pages 391–397
DOI: https://doi.org/10.1007/s10958-007-0448-z
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: English
Citation: R. I. Grigorchuk, V. V. Nekrashevych, “Amenable actions of nonamenable groups”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Zap. Nauchn. Sem. POMI, 326, POMI, St. Petersburg, 2005, 85–96; J. Math. Sci. (N. Y.), 140:3 (2007), 391–397
Citation in format AMSBIB
\Bibitem{GriNek05}
\by R.~I.~Grigorchuk, V.~V.~Nekrashevych
\paper Amenable actions of nonamenable groups
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XIII
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 326
\pages 85--96
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl339}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2183217}
\zmath{https://zbmath.org/?q=an:1127.43001}
\elib{https://elibrary.ru/item.asp?id=9127010}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 140
\issue 3
\pages 391--397
\crossref{https://doi.org/10.1007/s10958-007-0448-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33845766312}
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  • https://www.mathnet.ru/eng/znsl/v326/p85
    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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