English

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.

Keywords

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

R2 v1 2026-06-22T18:04:42.327Z