Notes on the commutator group of the group of interval exchange transformations

TL;DR

This paper investigates the structure of the commutator group within the group of interval exchange transformations, revealing that it is generated by elements of order 2 and providing multiple characterizations.

Contribution

It offers new characterizations of the commutator group and shows it is generated by involutions, advancing understanding of the algebraic structure of interval exchange transformations.

Findings

The commutator group is generated by elements of order 2.

Multiple characterizations of the commutator group are provided.

The structure of the commutator group is clarified within the context of interval exchange transformations.

Abstract

We study the group of interval exchange transformations and obtain several characterizations of its commutator group. In particular, it turns out that the commutator group is generated by elements of order 2.