The Hopf Property for Subgroups of Hyperbolic Groups
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- Bumagina, I. Geometriae Dedicata (2004) 106: 211. doi:10.1023/B:GEOM.0000033859.35966.4a
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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).