Discreteness of subgroups of $\mathrm{SL}(2,\boldsymbol{C})$ containing elliptic elements

Abstract

The following result is the main result of the paper. Let $G\subset \boldsymbol{SL}(2,\boldsymbol C)$ be non-elementary. If $G$ contains an elliptic element of order at least 3, then $G$ is discrete if and only if each non-elementary subgroup generated by two elliptic elements of $G$ is discrete.