Groups generated by two elliptic elements in PU(2,1)

Abstract

Let $f$ and $g$ be two elliptic elements in $\mathbf{PU}(2,1)$ of order $m$ and $n$ respectively, where $m\ge n>2$. We prove that if the distance $\delta (f,g)$ between the complex lines or points fixed by $f$ and $g$ is large than a certain number, then the group $<f,g>$ is discrete nonelementary and isomorphic to the free product ${\mathbf{Z}}_m\ast {\mathbf{Z}}_n$.

9 pages

References in corpus (1)

• Complex hyperbolic triangle groups