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Nielsen methods and groups acting on hyperbolic spaces

Ilya Kapovich·Richard Weidmann
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Abstract

We show that for any positive integer $n$ there exists a constant $C(n)>0$ such that any $n$-generated group $G$, which acts by isometries on a $δ$-hyperbolic space (with $δ>0$), is either free or has a nontrivial element with translation length at most $δC(n)$.

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Ilya Kapovich, Richard Weidmann. 2002-03-02. Nielsen methods and groups acting on hyperbolic spaces. https://arxiv.org/abs/math/0203014

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