Elementary equivalence vs commensurability for hyperbolic groups
Group Theory
2019-06-07 v1 Logic
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.
Cite
@article{arxiv.1701.08853,
title = {Elementary equivalence vs commensurability for hyperbolic groups},
author = {Vincent Guirardel and Gilbert Levitt and Rizos Sklinos},
journal= {arXiv preprint arXiv:1701.08853},
year = {2019}
}
Comments
19 pages