Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sbornik: Mathematics, 2014, Volume 205, Issue 6, Pages 843–861
DOI: https://doi.org/10.1070/SM2014v205n06ABEH004400
(Mi sm8257)
 

This article is cited in 20 scientific papers (total in 20 papers)

On algebraic properties of topological full groups

R. Grigorchukab, K. Medynetsc

a Steklov Mathematical Institute of Russian Academy of Sciences
b Texas A&M University
c United States Naval Academy
References:
Abstract: We discuss the algebraic structure of the topological full group $[[T]]$ of a Cantor minimal system $(X,T)$. We show that $[[T]]$ has a structure similar to a union of permutational wreath products of the group $\mathbb Z$. This allows us to prove that the topological full groups are locally embeddable into finite groups, give an elementary proof of the fact that the group $[[T]]'$ is infinitely presented, and provide explicit examples of maximal locally finite subgroups of $[[T]]$. We also show that the commutator subgroup $[[T]]'$, which is simple and finitely-generated for minimal subshifts, is decomposable into a product of two locally finite groups, and that $[[T]]$ and $[[T]]'$ possess continuous ergodic invariant random subgroups.
Bibliography: 36 titles.
Keywords: full group, Cantor system, finitely generated group, simple group, amenable group.
Funding agency Grant number
National Science Foundation DMS-1207699
Office of Naval Research N001613WX20992
Received: 11.06.2013 and 10.02.2014
Bibliographic databases:
Document Type: Article
UDC: 512.543+512.544+517.987
MSC: 20F65, 37B05
Language: English
Original paper language: Russian
Citation: R. Grigorchuk, K. Medynets, “On algebraic properties of topological full groups”, Sb. Math., 205:6 (2014), 843–861
Citation in format AMSBIB
\Bibitem{GriMed14}
\by R.~Grigorchuk, K.~Medynets
\paper On algebraic properties of topological full groups
\jour Sb. Math.
\yr 2014
\vol 205
\issue 6
\pages 843--861
\mathnet{http://mi.mathnet.ru//eng/sm8257}
\crossref{https://doi.org/10.1070/SM2014v205n06ABEH004400}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241829}
\zmath{https://zbmath.org/?q=an:06349853}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014SbMat.205..843G}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000344080300004}
\elib{https://elibrary.ru/item.asp?id=21826629}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84907363538}
Linking options:
  • https://www.mathnet.ru/eng/sm8257
  • https://doi.org/10.1070/SM2014v205n06ABEH004400
  • https://www.mathnet.ru/eng/sm/v205/i6/p87
  • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:583
    Russian version PDF:180
    English version PDF:24
    References:75
    First page:25
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024