Infinite groups
DOI10.1007/BF01091962zbMath0479.20001OpenAlexW4211233530MaRDI QIDQ1161607
Vladimir N. Remeslennikov, Guennadi A. Noskov, Vitaliĭ Roman'kov
Publication date: 1982
Published in: Journal of Soviet Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01091962
soluble groupsBibliographyperiodic groupsvarietiesresidually finite groupshomological methodsmodel-theoretic methodsfree constructionsrelatorsalgorithmic problems
Applications of logic to group theory (20A15) Solvable groups, supersolvable groups (20F16) Periodic groups; locally finite groups (20F50) Generators, relations, and presentations of groups (20F05) Homological methods in group theory (20J05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Residual properties and generalizations; residually finite groups (20E26) Quasivarieties and varieties of groups (20E10) Research exposition (monographs, survey articles) pertaining to group theory (20-02)
Related Items (4)
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- Some finitely generated, infinitely related metabelian groups with trivial multiplicator
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- The multiplicator of a splitting extension
- The cohomology of groups acting on trees
- The isomorphism problem for solvable groups
- Nilpotency class of a free group of the product of certain varieties
- A ten-term exact sequence in the homology of a group extension
- Some theorems of Hall type
- Uncountable universal locally finite groups
- Baer-invariants, isologism, varietal laws and homology
- Euler characteristics and characters of discrete groups
- The residual nilpotency of the augmentation ideal and the residual nilpotency of some classes of groups
- Embedding some interlacings in groups of automorphisms of finitely generated solvable groups
- Universal group with twenty-one defining relations
- Free groups are residually alternating of even degree
- Some residual properties of certain nilpotent-by-abelian groups
- Solvable torsion-free groups
- Decidability of the conjugacy problem does not carry over to finite extensions of groups
- A note on permutable subgroups
- Whitehead groups may be not free, even assuming CH. I
- Definability in algebraically closed systems
- Existentially closed structures and Jensen's principle \(\diamond\)
- A nonsimplicity criterion for groups
- Some infinite groups with a prescribed system of complemented infinite abelian subgroups
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- On finitely generated subgroups of free groups
- Subgroups of direct products
- Free subgroups of finitely presented groups
- Jacobi identity for groups
- Totally categorical groups and rings
- Local finiteness of certain groups with minimum condition for Abelian subgroups
- Mayer-Vietoris sequences for HNN-groups and homological duality
- Splitting of group extensions
- Unsolvability of the endomorphic reducibility problem in free nilpotent groups and in free rings
- Model theory
- A property of Suzuki groups
- Polycyclic Frattini factors in certain finitely generated groups
- The symmetries of classes of elements in a free group of rank two
- Cohomology of split group extensions
- Conjugacy in free polynilpotent groups
- Converse of a theorem of Mal'cev on nilpotent groups
- Note sur un théorème de Lipschutz
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- Group rings of polycyclic groups
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- On periodic groups with an almost regular involution
- Nielsen equivalence of presentations of some solvable groups
- Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam
- The lower central series of groups of a special class
- Soluble groups with the minimum condition for normal subgroups
- Generalizations of the classes of nilpotent and hypercentral groups
- On soluble min-by-max groups
- A subgroup characterisation of soluble min-by-max groups
- On exact sequences in the homology of groups and algebras
- Homological methods in group varieties
- Strong finiteness conditions in locally finite groups
- On the intersection of finitely generated subgroups of a free group
- The automorphism group of a polycyclic group
- A theorem on finitely generated hyperabelian groups
- On join varieties of groups
- Maximal subgroups and chief factors of certain generalized soluble groups
- The Hopf property of free products
- Generalised free products which are free products of locally extended residually finite groups
- Cohomological topics in group theory.
- On groups of exponent four
- Automorphism towers of polycyclic groups
- Small cancellation theory over free products with amalgamation
- Abelian factorizations of infinite groups
- Automorphism towers of extremal groups
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- Embeddings into hopfian groups
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- Subgroups of infinite index in Fuchsian groups
- A general solution of binary homogeneous equations over free groups
- The number of non-isomorphic models of an unstable first-order theory
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- Ends and amalgamated free products of groups
- Homology of a group extension
- Nondistributivity of the lattice of varieties of nilpotent groups
- Some isolated subsets of infinite solvable groups.
- Groups with normalizer conditions
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- On central group extensions and homology
- On relatively free groups which are similar to metabelian groups
- On the approximation of free groups
- On free products with amalgamation of two infinite cyclic groups
- Determination of locally finite groups with duals
- Cohomology of finitely presented groups
- Word problems and recursively enumerable degrees of unsolvability. An emendation
- Truth-table degrees and the Boone groups
- Note on independent equation problems in groups
- On 2-metabelian groups (addendum)
- On the homology theory of central group extensions. I: The commutator map and stem extensions
- Zur Frage nach dem Gitter der nilpotenten Varietäten von Gruppen der Klasse 4
- Über die cohomologische Dimension der auflösbaren Gruppen
- On a Theorem of Cohen and Lyndon About Free Bases for Normal Subgroups
- The soluble subgroups of a one-relator group with torsion
- Residually F p -Groups, for Many Primes p, are Orderable
- Subgroups with Almost-Complements
- The free centre-by-metabelian groups
- Sq-Universality in Hnn Groups and One Relator Groups
- Groups of dimension 1 are locally free
- One-Variable Equations in Free Groups
- Laws in Nilpotent-by-Finite Groups
- On Residual Nilpotence
- On the Residual Finiteness of Generalized Free Products
- Some varieties without the amalgam embedding property
- On certain abelian-by-nilpotent varieties
- A finite basis theorem for product varieties of groups
- Two-Generator Conditions for Polycyclic Groups
- Sylow Subgroups of Locally Finite Groups with Min-P
- On Embedding Groups and the Conjugacy Problem
- On Britton's Theorem A
- Root-Closure in Free Groups
- Critical Groups and the Lattice of Varieties
- Embeddings in Non-Hopf Groups
- Commutators of Certain Finitely Generated Soluble Groups
- Groups of Automorphisms of Soluble Groups
- Subgroups of amalgamated free products
- Note on the Homology of a Fiber Product of Groups
- Some symmetric varieties of groups
- On Greendlinger's lemma
- ABELIAN BY NILPOTENT VARIETIES
- Generating groups of nilpotent varieties
- Some product varieties of groups
- A residual property of free groups
- On Greendlinger groups
- Infinite groups whose proper quotient groups are finite, II
- On the laws of free nilpotent groups.
- A five lemma for free products of groups with amalgamations
- On soluble just-non-Cross varieties of groups
- On the laws of some varieties of groups
- On the Free Product of Two Groups with an Amalgamated Subgroup of Finite Index in each Factor
- On the Weak Homological Dimension of the Group Algebra of Solvable Groups
- On Metanilpotent Varieties of Groups
- Locally finite varieties of groups arising from Cross varieties
- Nilpotency and related properties of group extensions
- Finiteness Conditions in Generalized Soluble Groups
- On Groups of Exponent Four. II
- Torsion-Free Groups and Amalgamated Products
- A Free Resolution for a Class of Groups
- Groups with certain solvable and unsolvable decision problems
- On soluble groups of prime-power exponent
- Varieties of Metabelian p-Groups of Class b, p+1
- On Locally Finite Groups with Min-P
- On R0-Closed Classes, and Finitely Generated Groups
- Just non-finitely-based varieties of groups
- FINITE SPLITTING GROUPS IN VARIETIES OF GROUPS
- On Residually Finite Generalized Free Products
- Products of Abelian Subgroups
- Finitely generated cyclic extensions of free groups are residually finite
- Representations of Free Metabelian π -Groups
- Uncountably many Varieties of Groups
- On varieties of soluble groups
- A Bound for the Derived Length of Certain Polycyclic Groups
- On the residual finiteness of permutational products of groups
- Conjugacy Separability of Certain Free Products with Amalgamation
- A finitely generated, infinitely related group with trivial multiplicator
- Embedding Theorems for Countable Groups
- Unsolvable Problems in Groups With Solvable Word Problem
- A problem of Hanna Neumann on closed sets of group words
- Varieties of soluble groups and a dichotomy of P. Hall
- On Central Series of a Soluble Group
- On the isomorphism problem for just‐infinite groups
- On decomposable varieties of groups
- On Finitely Generated Subgroups of Free Products
- A nonsolvable group of exponent 5
- On product varieties of groups
- ON s-CRITICAL GROUPS
- On non-cross varieties of groups
- F -Abnormal Subgroups of Certain Locally Finite Groups
- Sylow Subgroups of Locally Finite Groups
- Third Engel groups and the Macdonald-Neumann conjecture
- Automorphisms of Group Extensions
- The Subgroups of a Free Product of Two Groups with an Amalgamated Subgroup
- On Finitely Generated Subgroups Which are of Finite Index in Generalized Free Products
- The Power Problem for Groups with One Defining Relator
- Subgroups of Conjugate Classes in Extensions
- On Free Groups of the Variety AN2 ∧ N2A
- Varieties of soluble groups
- Directly Decomposable Finite Relatively Free Groups
- A Class of Locally Finite Groups†
- The endomorphisms of certain one-relator groups and the generalized Hopfian problem
- A non-cyclic, locally free, free-by-cyclic group all of whose finite factor groups are cyclic
- Model-completions and modules
- An index of P. Hall for varieties of groups
- Dichotomies in Certain Finitely Generated Soluble Groups
- A Note on Root Decision Problems in Groups
- Residual Finiteness of Surface Groups
- Homology in varieties of groups. II
- On lattices of varieties of metabelian groups
- Subgroups of HNN Groups and Groups with one Defining Relation
- Representations of Some Relatively Free Groups in Power Series Rings
- The subnormal structure of metanilpotent groups
- The Hopficity of F/r′
- On $ω_1$-categorical theories of abelian groups
- Residual properties of free groups II
- On Centre-By-Metabelian Varieties of Groups
- On Locally Finite Varieties of Groups
- The skeleton of a variety of groups
- The subnormal structure of some classes of coluble groups
- Finitely Generated Subgroups of HNN Groups
- Normalizer Condition and Nilpotent Normal Subgroups
- On three-Engel groups
- On Groups of Exponent Four. III
- On conjugate powers in eighth-groups
- On the Freiheitssatz
- On One-Relator Groups Having Elements of Finite Order
- Conjugacy Separability of Certain Fuchsian Groups
- The computability of group constructions II
- A Note on Residual Properties of Nilpotent Groups
- On Products of Powers in Groups
- Nonresidually Finite One-Relator Groups
- Two Theorems in the Commutator Calculus
- On GL2(R) Where R is a Boolean Ring
- The Free Product of Two Groups with a Malnormal Amalgamated Subgroup
- The elementary theory of abelian groups
- Ends of Groups and the Associated First Cohomology Groups
- A Note on F-Reducibility
- Bases for Polynilpotent Groups
- The Eliminant of a Group
- On the laws of the variety se
- On varieties of metabelian groups of prime-power exponent
- FREE DECOMPOSITIONS IN VARIETIES OF Λ-GROUPS
- Relation Modules
- A Product Variety of Groups with Distributive Lattice
- On the Frattini Subgroups of Generalized Free Products with Cyclic Amalgamations(1)
- On the Frattini Subgroups of Certain Generalized Free Products of Groups
- A Conjugacy Theorem for Locally Finite Groups
- On finitely presented metabelian groups
- The Inflation Homomorphism
- Third-Engel 2-Groups are Soluble
- On the Finitely Generated Subgroups of an Amalgamated Product of Two Groups
- On Groups Satisfying Min-p
- On a Problem of Boone.
- On Outer-Commutator Words
- The Free Product of Residually Finite Groups Amalgamated Along Retracts is Residually Finite
- On non-Cross varieties of A-groups
- Normal Subgroups of Groups which are Products of Two Abelian Subgroups
- Normal subgroups of the modular group
- Finiteness conditions in soluble groups and Lie algebras
- Subgroups of free solvable groups
- A FREEDOM THEOREM FOR GROUPS WITH ONE DEFINING RELATION IN THE VARIETIES OF SOLVABLE AND NILPOTENT GROUPS OF GIVEN LENGTHS
- Soluble groups satisfying the minimal condition for normal subgroups
- Some Undecidable Problems in Group Theory
- Some model theory of abelian groups
- Some Results on Parafree Groups
- Groups of Automorphisms of Infinite Soluble Groups
- The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups
- A Finitely Generated Residually Finite Group with an Unsolvable Word Problem
- Sylowizers in Locally Finite Groups
- Free Subgroups of Small Cancellation Groups
- Factoring a group as an amalgamated free product
- Varieties and section closed classes of groups
- On torsion‐free nilpotent varieties
- Conjugacy Separating Representations of Free Groups
- Products of powers in groups
- Remarks on the localization of nilpotent groups
- Certain commutator subgroups of free groups
- A remark concerning commutator subgroups of free groups
- Martin's Axiom Applied to Existentially Closed Groups.
- A criterion for non‐solvability of exponent 4 groups
- The SQ-universality of some finitely presented groups
- A class of $\pi _c$ groups closed under cyclic amalgamations
- A Finitely Presented Metabelian Group with a Free Abelian Derived Group of Infinite Rank
- Letter to the editor
- Free products of Hopf groups
- Intersections of primary powers of a group
- Groups of cohomological dimension one
- Residual properties of free groups
- Automorphisms of solvable groups
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