Elementary equivalence vs. commensurability for hyperbolic groups
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- by Vincent Guirardel, Gilbert Levitt and Rizos Sklinos PDF
- Trans. Amer. Math. Soc. 371 (2019), 3397-3416 Request permission
Abstract:
We study to what extent torsion-free (Gromov)-hyperbolic groups are elementarily equivalent to their finite index subgroups. In particular, we prove that a hyperbolic limit group either is a free product of cyclic groups and surface groups or admits infinitely many subgroups of finite index which are pairwise non-elementarily equivalent.References
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Additional Information
- Vincent Guirardel
- Affiliation: Institut de Recherche Mathématique de Rennes, Université de Rennes 1 et CNRS (UMR 6625), 263 avenue du Général Leclerc, CS 74205, F-35042 Rennes Cédex, France
- MR Author ID: 631341
- Email: vincent.guirardel@univ-rennes1.fr
- Gilbert Levitt
- Affiliation: Laboratoire de Mathématiques Nicolas Oresme, Université de Caen et CNRS (UMR 6139), LMNO BP5186, 14032 Caen Cédex, France (Pour Shanghai : Normandie Université, UNICAEN, CNRS, LMNO, 14000 Caen, France)
- MR Author ID: 113370
- Email: levitt@unicaen.fr
- Rizos Sklinos
- Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1 (UMR 5208), 43 boulevard du 11 novembre 1918, 69622, Villeurbanne cedex, France
- MR Author ID: 929220
- Email: rizozs@gmail.com
- Received by editor(s): February 23, 2017
- Received by editor(s) in revised form: August 29, 2017
- Published electronically: December 7, 2018
- Additional Notes: This work was mainly conducted during the 2016 Oberwolfach workshop on Model Theory, for which the authors acknowledge support and hospitality.
The first author acknowledges support from the Institut universitaire de France.
The second author is grateful to the organizers of the 2015 Workshop on Model Theory and Groups in Istanbul for making him think about the topic studied here.
The third author was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR) - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 3397-3416
- MSC (2010): Primary 20F65, 20F67, 20F70
- DOI: https://doi.org/10.1090/tran/7392
- MathSciNet review: 3896116