The Hopf Property for Subgroups of Hyperbolic Groups
- Cite this article as:
- Bumagina, I. Geometriae Dedicata (2004) 106: 211. doi:10.1023/B:GEOM.0000033859.35966.4a
A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology35 (2) 1999, 301–321).