Finite generation for the group $F\left(\frac{3}{2}\right)$

In this paper it is proved that the group $F\left(\frac{3}{2}\right)$, a Thompson-style group with breaks in $\mathbb{Z}\left[\frac{1}{6}\right]$ but whose slopes are restricted only to powers of $\frac{3}{2}$, is finitely generated, with a generating set of two elements.