On the failure of the co-Hopf property for subgroups of word-hyperbolic groups

DOI10.1007/BF02809895zbMath0991.20031OpenAlexW2075346173MaRDI QIDQ5935804

Ilya Kapovich, Daniel T. Wise

Publication date: 2 May 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02809895

zbMATH Keywords

finitely generated groupshyperbolic groupsco-Hopfian groupsfreely indecomposable groupsgroup splittingsinjective endomorphismssmall cancellation theorytorsion-free word-hyperbolic groups

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Geometric group theory (20F65) Topological methods in group theory (57M07) Automorphisms of infinite groups (20E36) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Hyperbolic groups and nonpositively curved groups (20F67) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Related Items (8)

ENDOMORPHISMS OF RELATIVELY HYPERBOLIC GROUPS ⋮ Endomorphic presentations of branch groups. ⋮ Structure of normally and finitely non-co-Hopfian groups ⋮ A Sierpiński carpet with the co-Hopfian property ⋮ Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups. ⋮ Pro-groups and generalizations of a theorem of Bing ⋮ Hölder Conditions for Endomorphisms of Hyperbolic Groups ⋮ COSET ENUMERATION FOR CERTAIN INFINITELY PRESENTED GROUPS

Cites Work

• Endomorphisms of hyperbolic groups. I: The Hopf property
• Structure and rigidity in hyperbolic groups. I
• Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank \(1\) Lie groups. II
• Stable actions of groups on real trees
• Coherence, local quasiconvexity, and the perimeter of 2-complexes.
• Dehn's algorithm for the word problem
• Branched Coverings of Cubical Complexes and Subgroups of Hyperbolic Groups
• Subgroups of small Cancellation Groups
• Hyperbolic groups and free constructions
• Incoherent negatively curved groups
• Self-embeddings of Kleinian groups
• Subgroups of Word Hyperbolic Groups in Dimension 2
• Intersections of Finitely Generated Subgroups in Free Products
• The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the failure of the co-Hopf property for subgroups of word-hyperbolic groups