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.
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