On topologizable and non-topologizable groups

DOI10.1016/j.topol.2013.08.017zbMath1285.22003arXiv1210.7895OpenAlexW2047633591MaRDI QIDQ392820

Denis V. Osin, Anton A. Klyachko, Alexander Yu. Ol'shanskii

Publication date: 15 January 2014

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.7895

zbMATH Keywords

hyperbolic group\(c\)-compact group(hereditarily) non-topologizable groupTarski Monstertopologizable group

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Hyperbolic groups and nonpositively curved groups (20F67) Multiply transitive infinite groups (20B22)

Related Items (18)

c-minimal topological groups ⋮ Products of topological groups in which all closed subgroups are separable ⋮ Zariski topology and Markov topology on groups ⋮ Categorically proper homomorphisms of topological groups ⋮ On the lattice of \(f\)-subgroups ⋮ Predecessors and successors of the Euclidean topology on a subgroup of \(\mathrm{GL}(2,\mathbb{R})\) ⋮ Categorically closed countable semigroups ⋮ Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones ⋮ Absolutely closed semigroups ⋮ Topologizations of a set endowed with an action of a monoid ⋮ Algebraic subgroups of acylindrically hyperbolic groups ⋮ \(c\)-compactness in locally compact groups and paratopological groups ⋮ Topologizable structures and Zariski topology ⋮ Categorically closed topological groups ⋮ Acylindrically hyperbolic groups ⋮ Selective survey on spaces of closed subgroups of topological groups ⋮ Hereditarily minimal topological groups ⋮ Abstract homomorphisms from some topological groups to acylindrically hyperbolic groups

Cites Work

• Small cancellation in acylindrically hyperbolic groups
• Peripheral fillings of relatively hyperbolic groups.
• Small cancellations over relatively hyperbolic groups and embedding theorems.
• Categorically compact topological groups
• The space of finitely generated groups
• Acylindrically hyperbolic groups
• AN IMBEDDING THEOREM FOR GROUPS AND ITS COROLLARIES
• DEGREES OF GROWTH OF FINITELY GENERATED GROUPS, AND THE THEORY OF INVARIANT MEANS
• ON RESIDUALING HOMOMORPHISMS AND G-SUBGROUPS OF HYPERBOLIC GROUPS
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Topological groups with Rokhlin properties
• Local Properties of Systems
• The number of non-solutions of an equation in a group
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