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The Hopf Property for Subgroups of Hyperbolic Groups |
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| Authors: | Inna Bumagina |
| Institution: | (1) Department of Mathematics and Statistics, McGill University, 805, Sherbrooke Street West, Montreal, Que., Canada H3A 2K6; e-mail: |
| 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). |
| Keywords: | Mathematics Subject Classifications (2000) 20F67 57M07 Hyperbolic groups group action on real trees decompositions of groups endomorphisms of groups |
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