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arXiv · 1701.08853

Elementary equivalence vs commensurability for hyperbolic groups

Vincent Guirardel·Gilbert Levitt·Rizos Sklinos
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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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Vincent Guirardel, Gilbert Levitt, Rizos Sklinos. 2017-01-30. Elementary equivalence vs commensurability for hyperbolic groups. https://arxiv.org/abs/1701.08853

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