Dense subgroups in the group of interval exchange transformations

Abstract

The paper concerns the characterization of the group IET of interval exchange transformations (iet). We investigate a class of rational subgroups of 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 IET. We also discuss the properties of these groups.