On groups and fields interpretable in torsion-free hyperbolic groups

We prove that the generic type of a noncyclic torsion-free hyperbolic group G
is foreign to any interpretable abelian group, hence also to any interpretable field. This result depends, among other things, on the definable simplicity of a noncyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Sela’s description of imaginaries in torsion-free hyperbolic groups. We also use the description of imaginaries to prove that if F is a free group of rank > 2 then no orbit of a (nontrivial) finite tuple from F under Aut (F) is definable.