Is it true that all hyperbolic groups are finitely presented? If yes, what is the right reference for that?


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    $\begingroup$ Any book covering hyperbolic groups will have this result. If you prefer, you can refer to Gromov's "Hyperbolic Groups" essay. $\endgroup$ – Misha May 27 '16 at 8:35
  • $\begingroup$ I believe that Gromov's original definition included groups that are not finitely generated, and he called them word hyperbolic if they are. (See discussion here: mathoverflow.net/questions/233957) It is true and easy to prove that finitely generated hyperbolic groups are finitely presented. $\endgroup$ – Derek Holt May 27 '16 at 9:26