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 On groups and fields interpretable in torsion-free hyperbolic groups


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We prove that the generic type of a non-cyclic 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 non-cyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Selas 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 finite tuple from F under AutF is definable.



Author: ChloƩ Perin; Anand Pillay; Rizos Sklinos; Katrin Tent

Source: https://archive.org/







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