Topological groups

DOI10.1007/BF02105456zbMath0566.22003OpenAlexW4211228775MaRDI QIDQ1059160

Yu. N. Mukhin

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1007/bf02105456

zbMATH Keywords

finitenesssubgroupsvarietiesmorphismscommutativitydiscretenessgroup topologies

Mathematics Subject Classification ID

Structure of general topological groups (22A05)

Cites Work

• On Pure Subgroups of LCA Groups
• On the Automorphism Group of a Lie Group
• Free Topological Groups with no Small Subgroups
• Compatible Group Topologies
• Shorter Notes: On the Difference of Two Second Category Baire Sets in a Topological Group
• Kernels of Homomorphisms of Topological Groups
• On Deformations of Homomorphisms of Locally Compact Groups
• Shorter Notes: Representations of Almost Connected Groups
• A remark on free topological groups with no small subgroups
• Some examples of monothetic groups
• Lie groups in varieties of topological groups
• Countable products and sums of lines and circles: their closed subgroups, quotients and duality properties
• Subgroups of Free Topological Groups and Free Topological Products of Topological Groups
• Duality Theory for Locally Compact Groups With Precompact Conjugacy Classes. II: The Dual Space
• Closed Subgroups of Products of Reals
• Topologies in Locally Compact Groups, III
• A Schreier theorem for free topological groups
• Free k-groups and free topological groups
• Relationships between group topologies
• Inconsistent and Incomplete Logics
• The 5^th Hilbert‐Problem
• A Uniqueness Result for Topological Groups
• (CA) Topological Groups
• Fixed Points of Automorphisms
• Subgroups of the Free Topological Group on [0, 1]
• Compactness of Certain Homogeneous Spaces of Locally Compact Groups
• Compactness Properties of Topological Groups. III
• The coproduct of two circles
• The Free Topological Group on a Simply Connected Space
• A separable normal topological group need not be Lindelöf
• Uniqueness of Topology for the p-Adic Integers
• On Torsion Subgroups of Lie Groups
• Locally Compact Subgroups of Metrizable Topological Abelian Groups
• Uniform Structure in Topological Groups
• Reductivity and the Automorphism Group of Locally Compact Groups
• Applications of the Stone-Cech Compactification to Free Topological Groups
• On a Compactness Property of Topological Groups
• On polythetic groups
• Local compactness and local invariance of free products of topological groups
• On the Density Character of Closed Subgroups
• Topologically Semisimple Groups
• The Commutator Subgroup of a Free Topological Group Need Not be Projective
• A Note on Free Topological Groupoids
• Totally-disconnected compact metric groups
• Uniqueness in Structure Theorems for LCA Groups
• An analog of the two-dimensional local limit theorem
• Group Extensions and Cohomology for Locally Compact Groups. III
• Group Extensions and Cohomology for Locally Compact Groups. IV
• Reflexivity of Topological Groups
• The ideal structure of the Stone-Čech compactification of a group
• Tall profinite groups
• Fuglede's Theorem and Limits of Spectral Operators
• On epimorphisms of topological groups
• Embeddings in contractible or compact objects
• Continuity of homomorphisms
• Existence of compact totally disconnected groups with a locally compact but noncompact group of topological automorphisms
• The topological isolator of a subgroup of finite rank
• Estimate of the rank of connected locally compact nilpotent groups
• Kompaktheitseigenschaften der Gruppe der Isometrien metrischer Räume
• On products of subgroups in polycyclic groups
• Expansive automorphisms of locally compact solvable groups
• Locally compact groups of finite rank
• Profinite groups and Boolean graphs
• Dualisms of topological abelian groups
• Topological groups with compact lattice of closed subgroups
• Amenable subgroups of semi-simple groups and proximal flows
• Normal automorphisms of free profinite groups
• Linearly compact groups
• Minimally weakly almost periodic groups
• Normal automorphisms of absolute Galois groups of p-adic fields
• Compact torsion groups and finite exponent
• Topological nilgroups of matrices
• Gruppentopologien auf nichtabelschen abzählbaren Gruppen
• Die Norm lokal kompakter Gruppen
• On locally compact wreath products
• Eine Bemerkung zur Nilpotenz lokal kompakter Gruppen
• Topologische Gruppen mit endlichen Klassen konjugierter Elemente
• Invariant means on a locally compact group
• Compactness in Abelian topological groups
• Groups with completely regular primitive dual space
• Inverse limits and the completeness of quotient groups
• A characterization of Pontryagin duality
• Einige Sätze über unendlich teilbare Wahrscheinlichkeitsmaße auf lokalkompakten Gruppen
• Continuous measures, Baire category, and uniform continuity in topological groups
• A note on reduced duals of certain locally compact groups
• The type structure of the regular representation of a locally compact group
• Compactly cogenerated LCA groups
• Free products in the category of \(k_\omega\)-groups
• Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen
• Locally compact group topologies on an algebraic free product of groups
• On certain types of groups of rank one
• Lie algebras associated with topological nilpotent groups
• Compactness conditions in topological groups
• The Baire set fixing property and uniform continuity in topological groups
• Density character in topological groups
• One parameter subgroups and nonstandard analysis
• Lokal kompakte Gruppen mit gleichmäßig beschränkten Konjugiertenklassen
• On density properties of certain subgroups of locally compact groups
• Interval of group topologies satisfying Pontryagin duality
• Fitting subgroups and profinite completions of polycyclic groups
• Some minimal group topologies are precompact
• Non standard analysis and the compactification of groups
• The union of compact subgroups of a connected locally compact group
• Point processes with a conditionally independent uniform distribution of points on intervals
• Torsionskompakte Gruppen
• Some theorems on (CA) analytic groups. II
• Automorphismengruppen diskreter Gruppen als topologische Gruppen
• Some examples in connection with Pontryagin's duality theorem
• On the commutator subgroup of a nonconnected central group
• Topological groups which satisfy an open mapping theorem
• On the continuity of group operations
• Topologisch quasihamiltonsche Gruppen
• On \(L\)-subgroups of locally compact groups
• On the topology and geometry of arcwise connected, finite-dimensional groups
• Weak Frobenius reciprocity and compactness conditions in topological groups
• Examples of locally compact non-compact minimal topological groups
• Classes of nonabelian, noncompact, locally compact groups
• Coproducts of topological Abelian groups
• A question concerning CZ-groups
• An example of a Q-minimal precompact topological group containing a nonminimal closed normal subgroup
• Topological groups with invariant centralizers of elements
• Remarks on the free product of two Hausdorff groups
• On prosupersolvable groups
• Projections of abelian topological groups
• Finitely generated, connected groups
• Estimate of the rank of locally compact, solvable groups
• Quasinormalität in topologischen Gruppen
• Infinite Abelian groups are highly topologizable
• Untersuchungen zur Kommutatorgruppe in zentralen und kompakten topologischen Gruppen. II
• Extensions of Pontryagin duality
• The topology of compact simple Lie groups is essentially unique
• Specker--Kompaktifizierungen von lokal kompakten topologischen Gruppen
• Factorization of locally compact Abelian groups
• Die topologische Struktur des Raumes der Epimorphismen kompakter Gruppen
• Multipliers on Abelian groups
• Zur Theorie der Gruppen mit Untergruppentopologie
• Inverse Limites von Funktoren auf Kategorien kompakter Räume. Existenz- und Konjugiertensätze für kompakte Gruppen
• A structural property of certain locally compact Abelian groups
• Homomorphic images of Lie groups
• Über das Nilradikal lokal kompakter Gruppen
• Pseudocompact groups
• Erweiterungen kompakter Gruppen durch abelsche Gruppen
• On sequential convergence in groups
• Categories with convergence, exponential functors, and the cohomology of compact abelian groups
• Lokal kompakte Gruppen mit distributivem Verband abgeschlossener Untergruppen
• One dimensional coset spaces
• On the group of automorphisms of a finite-dimensional topological group
• Klassen zusammenhängender Gruppen
• Topologies in locally compact groups
• Über gewisse Verbände von Untergruppen pro-endlicher Gruppen
• Über die Zusammenhangskomponente des Neutralelements einer kompakten Gruppe
• Dualitätstheorie der nichtkommutativen Gruppen mit Normalteilertopologie
• Subnormalität in topologischen Gruppen
• On products of profinite groups
• On the Structure of Maximally Almost Periodic Groups.
• Varieties of topological groups III
• Note on Linearly Compact Abelian Groups
• Many Topological Abelian Groups Have Dense Divisible Subgroups
• On Subgroups of the First Kind.
• Locally Compact Topologies for Groups
• Representation Theory of Central Topological Groups
• A Frobenius‐ Wielandt Theorem for Compact Groups
• A Certain Type of Locally Compact Totally Disconnected Topological Groups
• Groups with Equal Uniformities
• Finite subgroups of locally compact groups
• A Note on Second Category Topological Groups
• A Characterization of Unitary Duality
• Structure of self dual torsion free metric LCA groups
• Expansive transformation semigroups of endomorphisms
• Some Remarks on Self-Dual Locally Compact Abelian Groups
• Non-archimedian metrizability of topological groups
• Free products of topological groups
• Amenable Subsemigroups of a Locally Compact Group
• Dimensionality and the Duals of Certain Locally Compact Groups
• On Compactification and Structure of Topological Groups
• A note on the structure of Moore groups
• On Existence of Compact Open Normal Subgroups of 0-Dimensional Groups
• Epimorphisms of Compact Groups are Onto
• Compactness in Hom(G, H)
• A Finiteness Condition for Locally Compact Abelian Groups
• On Expansive Transformation Groups
• Compact Group Topologies for R
• On locally compact abelian groups which are topologically pure in their Bohr compactifications
• Quotient Groups of Topological Groups with No Small Subgroups
• Construction of group topologies on abelian groups
• Can an LCA Group be Anti-Self-Dual?
• On the sum and difference of two sets in topological vector spaces
• Semidirect Products of Topological Groups with Equal Uniformities
• Mapping properties of characters of LCA groups
• Verallgemeinerte Graphensätze für topologische Gruppen
• Dense Subgroups of Compact Groups
• Nets of Subgroups and Amenability
• Torsion topological groups with minimal open sets
• Extensions of locally compact abelian groups. I
• Functorial Characterizations of Pontryagin Duality
• Borel Structures in Groups and Semigroups.
• Well-Known LCA Groups Characterized by their Closed Subgroups
• Sufficiency Classes of LCA Groups
• On varieties of topological groups generated by solvable groups
• Compactness conditions in topological groups.
• Homological Study of Purity in Locally Compact Groups
• Locally Compact Abelian Groups and the Variety of Topological Groups Generated by the Reals
• [https://portal.mardi4nfdi.de/wiki/Publication:5628314 � -Projective Objects]
• Locally compact groups and β-varieties of topological groups
• A note onW-groups
• On the Limit of Subgroups in a Group
• Compactness Properties of Topological Groups
• Varieties of topological groups generated by Lie groups
• Generators of Monothetic Groups
• Closed Subgroups of a Locally Compact Group
• Compact Groups with Ordered Duals Iii
• k-Groups and Duality
• Varieties of topological groups generated by maximally almost periodic groups
• Groups with Finite Dimensional Irreducible Representations
• On theorems of Thornton
• A solenoidal and monothetic minimally almost periodic group
• Note on a theorem of Weil‐Abels
• Duality and von Neumann algebras
• On Countable Inductive Limits of Locally Compact Abelian Groups
• Splitting in Map Groups
• Completions of topological Abelianp-groups
• Topologically Complete Groups
• Topological Dynamics and Group Theory
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• Über eigentliche Transformationsgruppen
• Semimodular compact groups
• On conjugacy of homomorphisms of topological groups
• Über Automorphismengruppen lokal-kompakter Gruppen und Derivationen von Lie-Gruppen
• A duality theorem for locally compact groups. I - IV
• Projektive Limites kompakter Räume
• Supplements for the identity component in locally compact groups
• On local connectedness of locally compact Abelian groups
• Representative functions on topological groups
• On the topology of a dual space
• Endomorphism near-ring of a relatively free group
• Verbände vertauschbarer Untergruppen
• The adjoint group of Lie groups
• Kompakte Subnormalteiler
• Locally compact, totally disconnected, solvable groups
• Dualität lokalkompakter Gruppen
• duality and subgroups
• The automorphism group of a locally compact group
• Minimal topological groups
• Locally compact abelian groups with trivial multiplier group
• Pseudocompactness and uniform continuity in topological groups
• Complete lattices of subgroups in compact groups
• Locally compact topologies on a group and the corresponding continuous irreducible representations
• On conjugacy of homomorphisms of topological groups. II
• On CA topological groups
• On (CA) topological groups. II
• Group extensions by totally disconnected groups
• The automorphism group of a locally compact Abelian group
• Note on the open mapping theorem
• Kompakt definierbare topologische Gruppen. (Compactly definable topological groups)
• On the asymptotic spectrum of nonsmooth elliptic equations
• A remark on finite dimensional compactifications
• On p-thetic groups
• Splitting locally compact abelian groups
• Locally compact abelian groups of finite rank
• A subgroup theorem for free products of pro-finite groups
• Erratum: On the Bohr compactification
• Normen auf freien topologischen Gruppen. (Normes on free topological groups.)
• Groups with the minimality condition for the subgroups
• The Baire set fixing property in topological groups
• Sur les produits filtres de certains groupes topologiques
• Homogeneity or otherwise for certain morphism spaces
• Arcs in locally compact groups
• Extensions of topological groups
• Structure of monogenic groups
• Non-abelian Pontriagin duality
• Compactness properties of topological groups
• Compactness properties of topological groups. II
• Category theory applied to Pontryagin duality
• Absolutely closed Lie groups
• Duality and subgroups. II
• Growth of connected locally compact groups
• Sui gruppi abeliani ridotti che ammettono una unica topologia compatta
• Enden von Räumen mit eigentlichen Transformationsgruppen
• Topology in duals of SIN-groups
• Fixelemente von Automorphismen nulldimensionaler abelscher Gruppen
• Discontinuous characters and subgroups of finite index
• Untersuchung zu Kommutatorgruppen und Bohrkompaktifizierung in zentralen und kompakten Gruppen
• Topologies in locally compact groups. II
• Paracompact topological groups and uniform continuity
• Der Schursche Multiplikator topologischer Gruppen
• On the Bohr compactification
• Zerfällung topologischer Gruppen
• Connectedness properties of locally compact groups
• Uniqueness of the Topology in Certain Compact Groups
• Sur la cohomologie continue des groupes localement compacts
• Continuity properties of compact right topological groups
• The von Neumann Kernel and Minimally Almost Periodic Groups
• On extensions of locally compact groups and unitary groups.
• The structure of connected LP -groups with finite-dimensional Lie algebra Dedicated to the 25th Anniversary of the G.D.R.
• The Category of Generalized Lie Groups
• K-Groups Generated by K-Spaces
• Dual Spaces of Groups with Precompact Conjugacy Classes
• On the structure of connected locally compact groups
• On Pontryagin duality
• A distal property of groups and the growth of connected locally compact groups
• Eine Bemerkung über lokalkompakte abelsche Gruppen
• CHABAUTY- und WEIL-Räume topologischer Gruppen
• Dense Subgroups of Lie Groups. II
• On the frattini subgroup of free products of profinite groups
• Norms on Free Topological Groups
• Finiteness theorems for polycyclic groups
• ON LOCALLY FINITE CZ-GROUPS
• Free topological groups
• Some Nonprojective Subgroups of Free Topological Groups
• A Note on Groups with Relatively Compact Conjugacy Classes
• Fixed points of endomorphisms of compact groups
• A Kurosh Subgroup Theorem for Free Pro--Products of Pro--Groups
• The free topological group on a cell complex
• Free Products of Topological Groups Which are k ω -Spaces
• Almost Locally Invariant Topological Groups
• Ends of locally compact groups and their coset spaces
• Varieties of topological groups and left adjoint functors
• Some Theorems on (CA) Analytic Group
• Tensorprodukte lokal kompakter abelscher Gruppen.
• Topological wreath products
• Closed subgroups of locally compact Abelian groups
• Free products of compact general algebras
• Einige Bemerkungen über der Raum der abgeschlossenen Mengen
• Direct limits of topological spaces and groups
• Expansive Automorphisms in Compact Groups.
• On central topological groups
• On Central Topological Groups
• Tensor products of topological Abelian groups.
• Topological Groups with Equal Left and Right Uniformities
• Projective Topological Groups
• On Extensions of Locally Compact Groups
• THE EXISTENCE OF A TOPOLOGICAL GROUP WITH AUTOMORPHISM GROUP C₇
• A Note on Positively Expansive Endomorphisms.
• Homological Algebra in Locally Compact Abelian Groups
• Amenable Groups and Groups with the Fixed Point Property
• Connectivity, Divisibility, and Torsion
• Lattices and the Adjoint Group of a Lie Group
• The Connectedness of Fundamental Sets
• Compactification and Duality of Topological Groups
• The Existence of Homomorphisms in Compact Connected Abelian Groups
• A characterization of multiplicative linear functionals in complex Banach algebras
• Allied Subsets of Topological Groups and Linear Spaces
• Splitting in topological groups
• On a closed graph theorem for topological groups
• Topological Groups and the Closed-Graph Theorem
• On self dual 𝐿𝐶𝐴 groups
• Über den Zusammenhang zwischen den Kompaktifizierungen einer topologischen Gruppe und den Kompaktifizierungen ihrer Normalteiler und Faktorgruppen
• On the structure of maximally almost periodic groups
• Some properties of locally compact groups
• Varieties of topological groups
• Über eine Kompaktifizierung topologischer Gruppen. II.
• Projective Profinite Groups
• Varieties of topological groups II
• Every Locally Compact Map Group is Unimodular
• Zur Bohr-Konvergenz von Folgen.
• Embedding a Transformation Group in an Automorphism Group
• A note on the duality of locally compact groups
• On Connectivity Properties of Finite-Dimensional Groups
• The Additive Structure of Integer Groups and p-Adic Number Fields
• Invariant metrics on free topological groups
• On Q-Dense and Densely Divisible LCA Groups
• The Projective Dimension of a Compact Abelian Group
• Homeomorphism and Isomorphism of Abelian Groups
• Remark on my Paper "Generators of Monothetic Groups"
• On Centralizers of Generalized Uniform Subgroups of Locally Compact Groups
• On the Homomorphisms of Locally Compact Groups
• A characterization of growth in locally compact groups
• Free Topological Groups and the Projective Dimension of a Locally Compact Abelian Group
• Generating varieties of topological groups
• Varieties of topological groups generated by solvable and nilpotent groups
• Compactness in locally compact groups
• Locally Compact Groups Without Distinct Isomorphic Closed Subgroups
• Spaces of closed subgroups of a connected Lie group
• Nilpotent Topological Groups
• Topologies in Free Algebras
• Unrestricted Free Products, and Varieties of Topological Groups
• On the isomorphism of topological groups
• Automorphism groups of compact, totally disconnected, nilpotent groups
• Topological properties of the lattice of subgroups
• Subgroups of finite index in profinite groups
• Subgroups of finite index in profinite groups
• Ergodic automorphisms and affine transformations of locally compact groups
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