On abstract commensurators of groups

DOI10.1515/JGT.2010.021zbMath1262.20046arXiv0902.4542OpenAlexW3102517079MaRDI QIDQ3068142

Laurent Bartholdi, O. V. Bogopol'skij

Publication date: 13 January 2011

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.4542

zbMATH Keywords

free products with amalgamationHNN extensionsautomorphism groupsfree groupssurface groupsword-hyperbolic groupsabstract commensuratorsgroups with unique rootsisomorphisms between subgroups of finite indexnon-extendable automorphisms

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Automorphism groups of groups (20F28) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (10)

Abstract Commensurators of Solvable Baumslag–Solitar Groups ⋮ Commensurations of the outer automorphism group of a universal Coxeter group ⋮ Nilpotent algebras, implicit function theorem, and polynomial quasigroups ⋮ Generalized torsion, unique root property and Baumslag-Solitar relation for knot groups ⋮ Commensurators of finitely generated nonfree Kleinian groups. ⋮ New Simple Lattices in Products of Trees and their Projections ⋮ On universal minimal proximal flows of topological groups ⋮ Abstract commensurators of surface groups ⋮ Commensurations of subgroups of 𝑂𝑢𝑡(𝐹_{𝑁}) ⋮ On invariant von Neumann subalgebras rigidity property

Cites Work

• Commensurability classes of 2-bridge knot complements
• On the rank of amalgamated products and product knot groups
• Abstract commensurators of groups acting on rooted trees.
• Very small group actions on \(\mathbb{R}\)-trees and Dehn twist automorphisms
• On the Bass-Lubotzky question about quotients of hyperbolic groups
• Abstract commensurators of braid groups.
• On infinite complete groups

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