, Volume 106, Issue 1, pp 211-230

The Hopf Property for Subgroups of Hyperbolic Groups

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Abstract

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 (Topology 35 (2) 1999, 301–321).