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Algebra Discrete Math., 2014, Volume 17, Issue 2, Pages 232–247 (Mi adm468)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

Dense subgroups in the group of interval exchange transformations

Agnieszka Bier, Vitaliy Sushchansky

Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland

Abstract: The paper concerns the characterization of the group $\mathop{IET}$ of interval exchange transformations (iet). We investigate a class of rational subgroups of $\mathop{IET}$. These are subgroups consisting of iet transformations defined by partitions with rational endpoints. We propose a characterization of rational subgroups in terms of infinite supernatural numbers and prove that every such subgroup is dense in $\mathop{IET}$. We also discuss the properties of these groups.

Keywords: Interval exchange transformations, rational subgroups, dense subgroups, supernatural numbers.

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Bibliographic databases:
MSC: 37B05, 28D05, 37A05
Received: 25.03.2014
Revised: 25.03.2014
Language:

Citation: Agnieszka Bier, Vitaliy Sushchansky, “Dense subgroups in the group of interval exchange transformations”, Algebra Discrete Math., 17:2 (2014), 232–247

Citation in format AMSBIB
\Bibitem{BieSus14}
\by Agnieszka~Bier, Vitaliy~Sushchansky
\paper Dense subgroups in the group of interval exchange transformations
\jour Algebra Discrete Math.
\yr 2014
\vol 17
\issue 2
\pages 232--247
\mathnet{http://mi.mathnet.ru/adm468}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3287931}


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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. Oksana Bezushchak, Bogdana Oliinyk, Vitaliy Sushchansky, “Representation of Steinitz's lattice in lattices of substructures of relational structures”, Algebra Discrete Math., 21:2 (2016), 184–201  mathnet  mathscinet
  • Algebra and Discrete Mathematics
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