Elementary embeddings in torsion-free hyperbolic groups

By Chloé Perin. 2009

51 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b41a396ca5a0bdf12fbfca5608d7de1ab92fc735

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In Computational Theory and Mathematics

1. Vincent Guirardel
2. Gilbert Levitt
3. Abderezak Ould Houcine
4. Franccois Dahmani
5. Radhika Gupta
6. Benjamin Brück
7. E. Troitsky
8. Alexander Fel'shtyn

In Geometry and Topology

1. Vincent Guirardel
2. Gilbert Levitt
3. Abderezak Ould Houcine
4. Alessandro Sisto
5. Henry Wilton
6. Franccois Dahmani
7. Denis V. Osin
8. Michael Hull

In Mathematical Physics

1. Gilbert Levitt
2. Vincent Guirardel
3. Abderezak Ould Houcine
4. Franccois Dahmani
5. Alessandro Sisto
6. Henry Wilton
7. Denis V. Osin
8. Radhika Gupta

Citations in the corpus

• Homogeneity and prime models in torsion-free hyperbolic groups (2010, background): “([29, Proposition 5.12]) Let Γ be a torsion-free hyperbolic group.”
• Jsj Decompositions of Groups (2016, background): “xists a finite family H0= fH 1;:::;H pg, with H i a finitely generated group contained in a group of H, such that Gdoes not split over subgroups of orderCrelativetoH0. Aspecialcaseofthislemmaisprovedin[Per11]. Proof. All trees in this proof will have stabilizers in the family A(C) consisting of all su”