On groups and fields interpretable in torsion-free hyperbolic groups
Logic
2013-02-20 v2 Group Theory
Abstract
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 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 finite tuple from F under Aut(F) is definable.
Keywords
Cite
@article{arxiv.1210.5757,
title = {On groups and fields interpretable in torsion-free hyperbolic groups},
author = {Chloé Perin and Anand Pillay and Rizos Sklinos and Katrin Tent},
journal= {arXiv preprint arXiv:1210.5757},
year = {2013}
}
Comments
12 pages