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Elementary equivalence vs commensurability for hyperbolic groups (1701.08853v1)
Published 30 Jan 2017 in math.GR and math.LO
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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