The Maximality of $T$ in Thompson's group $V$

TL;DR

This paper proves that Thompson's group T is a maximal subgroup of V, using foundational calculations involving elements expressed as products of transpositions in Cantor space.

Contribution

It establishes the maximality of T in V and provides foundational methods for expressing elements of V as products of transpositions.

Findings

Thompson's group T is a maximal subgroup of V.

Provides methods for expressing elements of V as products of transpositions.

Includes foundational calculations related to Cantor space.

Abstract

We show that R. Thompson's group $T$ is a maximal subgroup of the group $V$. The argument provides examples of foundational calculations which arise when expressing elements of $V$ as products of transpositions of basic clopen sets in Cantor space $\mathfrak{C}$.