@misc{Bier_Agnieszka_Dense, author={Bier, Agnieszka and Sushchanskyy, Vitaliy}, howpublished={online}, language={eng}, 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.}, title={Dense subgroups in the group of interval exchange transformations}, keywords={tasowanie przedziału, podgrupa wymierna, podgrupa gęsta, liczby supernaturalne}, }