Elementary equivalence vs commensurability for hyperbolic groups

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.
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Submitted on : Friday, February 3, 2017 - 10:54:32 AM
Last modification on : Thursday, February 7, 2019 - 5:11:24 PM

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Vincent Guirardel, Gilbert Levitt, Rizos Sklinos. Elementary equivalence vs commensurability for hyperbolic groups. Transactions of the American Mathematical Society, American Mathematical Society, 2019, 371 (5), pp.3397-3416. ⟨10.1090/tran/7392⟩. ⟨hal-01454986⟩

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