Finite generation for the group $F\left(\frac32\right)$

TL;DR

This paper proves that the Thompson-style group $F(3/2)$, with slopes restricted to powers of 3/2 and breaks in a specific set, is finitely generated by two elements, expanding understanding of its algebraic structure.

Contribution

It establishes finite generation of the group $F(3/2)$ with a minimal generating set of two elements, a novel result in the study of such groups.

Findings

$F(3/2)$ is finitely generated.

A generating set of two elements suffices.

The group has a specific algebraic structure.

Abstract

In this paper it is proved that the group $F\left(\frac32\right)$, a Thompson-style group with breaks in $\mathbb{Z}\left[\frac16\right]$ but whose slopes are restricted only to powers of $\frac32$, is finitely generated, with a generating set of two elements.