On the automorphism group of generalized Baumslag-Solitar groups.

DOI10.2140/gt.2007.11.473zbMath1143.20014arXivmath/0511083OpenAlexW2132385066MaRDI QIDQ873947

Gilbert Levitt

Publication date: 21 March 2007

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511083

zbMATH Keywords

finitely generated groupsautomorphism groupsgroups acting on treesisomorphism problemouter automorphismsfinite index subgroupsfundamental groups of graphs of groupsgeneralized Baumslag-Solitar groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Automorphism groups of groups (20F28) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Groups acting on trees (20E08)

Related Items (37)

The Bass-Jiang group for automorphism-induced HNN-extensions ⋮ Free-by-cyclic groups, automorphisms and actions on nearly canonical trees ⋮ Vertex finiteness for splittings of relatively hyperbolic groups ⋮ The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups ⋮ Twisted conjugacy classes in twisted Chevalley groups ⋮ Cyclic amalgams, HNN extensions, and Garside one-relator groups ⋮ The \(R_\infty\)-property for right-angled Artin groups ⋮ The \(R_\infty\) property for pure Artin braid groups ⋮ The \(\mathrm{R}_\infty\)-property for nilpotent quotients of Baumslag-Solitar groups ⋮ Twisted conjugacy classes in nilpotent groups. ⋮ Testability in group theory ⋮ Group and algorithmic properties of generalized Baumslag-Solitar groups ⋮ Torsion in the outer automorphism groups of generalized Baumslag-Solitar groups ⋮ Stability for product groups and property \(( \tau )\) ⋮ A relationship between twisted conjugacy classes and the geometric invariants \(\Omega^n\). ⋮ Incommensurable lattices in Baumslag–Solitar complexes ⋮ The Schur multiplier of a generalized Baumslag-Solitar group. ⋮ Unnamed Item ⋮ On knot groups acting on trees ⋮ Cyclic normal subgroups of generalized Baumslag–Solitar groups ⋮ Embedding of Baumslag-Solitar groups into the generalized Baumslag-Solitar groups. ⋮ The isomorphism problem for generalized Baumslag-Solitar groups with one mobile edge ⋮ Twisted Conjugacy Classes for Polyfree Groups ⋮ Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups ⋮ New directions in Nielsen-Reidemeister theory ⋮ Certain residual properties of generalized Baumslag-Solitar groups ⋮ \( \mathcal{F}_\pi \)-residuality of generalized Baumslag-Solitar groups ⋮ On the isomorphism problem for generalized Baumslag-Solitar groups. ⋮ Invariants of orbit equivalence relations and Baumslag-Solitar groups ⋮ Twisted conjugacy classes in lattices in semisimple Lie groups ⋮ Generalized Baumslag-Solitar groups: rank and finite index subgroups ⋮ Quasi-isometric rigidity for graphs of virtually free groups with two-ended edge groups ⋮ Twisted conjugacy classes in nilpotent groups ⋮ Twisted conjugacy and commensurability invariance ⋮ On equivariant embeddings of generalized Baumslag-Solitar groups. ⋮ The Lipschitz metric on deformation spaces of \(G\)-trees ⋮ Commensurability of Baumslag-Solitar groups

Cites Work

• Unnamed Item
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• Splittings of generalized Baumslag-Solitar groups.
• A fixed point theorem for deformation spaces of \(G\)-trees.
• Deformation spaces of \(G\)-trees and automorphisms of Baumslag-Solitar groups.
• Moduli of graphs and automorphisms of free groups
• Automorphisms and Hopficity of certain Baumslag-Solitar groups
• Baumslag-Solitar groups and some other groups of cohomological dimension two
• Isomorphism of the Baumslag-Solitar groups
• Equivariant outer space and automorphisms of free-by-finite groups
• Quasi-actions on trees. I: Bounded valence
• A very short proof of Forester's rigidity result
• On uniqueness of JSJ decompositions of finitely generated groups.
• Deformation and rigidity of simplicial group actions on trees.
• The Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite.
• Deformation spaces of trees.
• The isomorphism problem for one-relator groups with non-trivial centre
• Contractibility of deformation spaces of \(G\)-trees.
• Automorphisms of hyperbolic groups and graphs of groups.
• Most automorphisms of a hyperbolic group have very simple dynamics
• A class of one-relator groups with centre
• Uniform Tree Lattices
• A note on centrality in 3-manifold groups
• Some two-generator one-relator non-Hopfian groups
• The Automorphism Towers of Some One-Relator Groups
• The automorphism group of a graph product of groups
• Local indicability in ordered groups: Braids and elementary amenable groups
• Virtually free groups with finitely many outer automorphisms
• Symmetric automorphisms of free products
• Tree actions of automorphism groups
• The outer space of a free product
• The large scale geometry of the higher Baumslag-Solitar groups

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