Details:
Definition: A class $\mathcal{G}$ of groups satisfies the Tits alternative if for any $G$ in $\mathcal{G}$ either $G$ has a free, non-abelian subgroup or $G$ has a solvable subgroup of finite index.
The Request:
I need a reference, please, for the theorem that hyperbolic groups satisfy the Tits Alternative.
(Please see the Wikipedia article linked to above for a definition of hyperbolic groups.)
Thoughts:
My guess is that it's
Gromov, Mikhail (1987). "Hyperbolic Groups". In Gersten, S.M. (ed.). Essays in Group Theory. Mathematical Sciences Research Institute Publications, vol 8. New York, NY: Springer. pp. 75–263.
It is from the hyperbolic groups Wikipedia page. I recognise the name from his other work (I think) in geometric group theory.
However, the paper is behind a paywall.
I require the reference for my research.
Please help 🙂
Best Answer
If you read French: Theorem 37, p. 157 in the book by Ghys and de la Harpe "Hyperbolic groups after Gromov".