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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

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

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
Revised: 25.03.2014
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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}