Dense subgroups in the group of interval exchange transformations

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.