Geometriae Dedicata

, Volume 106, Issue 1, pp 211–230

The Hopf Property for Subgroups of Hyperbolic Groups


  • Inna Bumagina
    • Department of Mathematics and StatisticsMcGill University, 805

DOI: 10.1023/B:GEOM.0000033859.35966.4a

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).

Mathematics Subject Classifications (2000).20F6757M07Hyperbolic groupsgroup action on real treesdecompositions of groupsendomorphisms of groups

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© Kluwer Academic Publishers 2004