Submission date: 30 January 2017

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.

Mathematics Subject Classification: 20F65, 20F70, 20F67

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Full text arXiv 1701.08853: pdf, ps.