Elementary equivalence vs commensurability for hyperbolic groups

Vincent Guirardel, Gilbert Levitt, Rizos Sklinos

Published 2017-01-30Version 1

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.