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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2019

Elementary equivalence vs commensurability for hyperbolic groups

Gilbert Levitt
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Rizos Sklinos
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Résumé

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.

Dates et versions

hal-01454986 , version 1 (03-02-2017)

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