{"paper":{"title":"On groups and fields interpretable in torsion-free hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.LO","authors_text":"Anand Pillay, Chlo\\'e Perin, Katrin Tent, Rizos Sklinos","submitted_at":"2012-10-21T19:46:24Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5757","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}