This article is cited 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.

MSC: 37B05, 28D05, 37A05

Received: 25.03.2014
Revised: 25.03.2014

Language: English

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