English

Elementary embeddings in torsion-free hyperbolic groups

Group Theory 2012-06-18 v3 Logic

Abstract

We consider embeddings in a torsion-free hyperbolic group which are elementary in the sense of first-order logic. We give a description of these embeddings in terms of Sela's hyperbolic towers. We deduce as a corollary that subgroups elementarily embedded in finitely generated free groups are free factors.

Keywords

Cite

@article{arxiv.0903.0945,
  title  = {Elementary embeddings in torsion-free hyperbolic groups},
  author = {Chloé Perin},
  journal= {arXiv preprint arXiv:0903.0945},
  year   = {2012}
}

Comments

The statement and the proof of Proposition 5.11 are corrected. All the other results remain unchanged

R2 v1 2026-06-21T12:18:36.488Z