Conjugacy class and discreteness in $\mathit{SL}(2, \mathbb{C})$

Abstract

In this note we establish a new discreteness criterion for a non-elementary group $G$ in $\mathit{SL}(2, \mathbb{C})$. Namely, $G$ is discrete if all the two-generator subgroups are discrete, where one generator is a non-trivial element $f$ in $G$, and the other is in the conjugacy class of $f$.