Zariski topology and Markov topology on groups

DOI10.1016/j.topol.2018.03.025zbMath1478.22002OpenAlexW2795297530WikidataQ130060972 ScholiaQ130060972MaRDI QIDQ1646545

Dikran Dikranjan, Daniele Toller

Publication date: 25 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.topol.2018.03.025

zbMATH Keywords

Zariski topologyMarkov topologyminimally almost periodic grouptopologizable groupcentralizer topologyvon Neumann kernelNoetherian spacenon-topologizable group

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Nilpotent groups (20F18) Free nonabelian groups (20E05) Algebraic geometry over groups; equations over groups (20F70)

Related Items

Categorically closed countable semigroups ⋮ Groups with cofinite Zariski topology and potential density ⋮ Absolutely closed semigroups ⋮ Lower continuous topological groups

Cites Work

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• Cardinal invariants distinguishing permutation groups
• On topologizable and non-topologizable groups
• Algebraically determined topologies on permutation groups.
• Homeomorphism groups of homogeneous compacta need not be minimal
• The Markov and Zariski topologies of some linear groups
• Finitely generated subgroups as von Neumann radicals of an abelian group
• Bounded subgroups as a von Neumann radical of an abelian group
• Topologizable groups. II
• The Markov-Zariski topology of an abelian group
• A Kronecker-Weyl theorem for subsets of Abelian groups.
• Characterization of almost maximally almost-periodic groups
• A complete solution of Markov's problem on connected group topologies
• A class of groups in which all unconditionally closed sets are algebraic.
• Which infinite abelian groups admit an almost maximally almost-periodic group topology?
• Some examples in connection with Pontryagin's duality theorem
• The verbal topology of a group
• Recent advances in minimal topological groups
• Nondiscrete topological groups with many discrete subgroups
• Compactness and connectedness in topological groups
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Categorically compact topological groups
• Chromatic numbers and Bohr topologies
• Independent group topologies on abelian groups
• A characterization of the maximally almost periodic abelian groups
• Countably compact groups satisfying the open mapping theorem
• Autohomeomorphism groups
• Topologizations of a set endowed with an action of a monoid
• w-divisible groups
• Unconditionally \(\tau \)-closed and \(\tau \)-algebraic sets in groups
• Closure operators in topological groups related to von Neumann's kernel
• Almost maximally almost-periodic group topologies determined by T-sequences
• Topological groups with many small subgroups
• Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology
• On the existence of free subgroups in topological groups
• On the imbedding of topological groups into connected topological groups
• A Short Solution of Markov's Problem on Connected Group Topologies
• TOPOLOGIES ON ABELIAN GROUPS
• Arnautov's problems on semitopological isomorphisms
• Some classes of minimally almost periodic topological groups
• Reflection principle characterizing groups in which unconditionally closed sets are algebraic
• Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov’s potential density
• Equations in free groups with one variable. I
• Almost Periodic Functions in a Group. I
• Minimally almost periodic group topologies on countably infinite Abelian groups
• Topological properties of Taimanov semigroups
• TOPOLOGICAL GROUP STRUCTURES OF INFINITE SYMMETRIC GROUPS
• A solenoidal and monothetic minimally almost periodic group
• The number of non-solutions of an equation in a group
• Topologies for Homeomorphism Groups
• Order and minimality of some topological groups