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

Baohua Xie; Yueping Jiang

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arXiv · 1003.2789

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

Baohua Xie·Yueping Jiang

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Abstract

Let $f$ and $g$ be two elliptic elements in $\mathbf{PU}(2,1)$ of order $m$ and $n$ respectively, where $m\geq n>2$. We prove that if the distance $δ(f,g)$ 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 $\mathbf{Z}_{m}*\mathbf{Z}_{n}$.

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Baohua Xie, Yueping Jiang. 2010-03-14. Groups generated by two elliptic elements in PU(2,1). https://arxiv.org/abs/1003.2789

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