Geometriae Dedicata

, Volume 106, Issue 1, pp 211-230

First online:

The Hopf Property for Subgroups of Hyperbolic Groups

  • Inna BumaginaAffiliated withDepartment of Mathematics and Statistics, McGill University, 805

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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).

Mathematics Subject Classifications (2000). 20F67 57M07 Hyperbolic groups group action on real trees decompositions of groups endomorphisms of groups