Some properties of a Magnus embedding

DOI10.1007/BF02321898zbMath0247.20026MaRDI QIDQ2555918

V. G. Sokolov, Vladimir N. Remeslennikov

Publication date: 1971

Published in: Algebra and Logic (Search for Journal in Brave)

Mathematics Subject Classification ID

Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Local properties of groups (20E25)

Related Items (35)

Decomposition of a group over an abelian normal subgroup ⋮ Algorithmic undecidability of compatibility problem for equations in free groups: explicit equations with one commutator-type constraint ⋮ On Embeddings of the Bachmuth Type ⋮ Some irreducible representations of automorphism groups of free groups ⋮ Right alternative algebras with commutators in a nucleus ⋮ The conjugacy problem in free solvable groups and wreath products of abelian groups is in \({\mathsf {TC}^0}\) ⋮ On the Magnus–Smelkin embedding ⋮ On splittings, subgroups, and theories of partially commutative metabelian groups ⋮ Some algorithmic problems for relatively free groups ⋮ The commutator width of elements in a wreath product of free Abelian groups. ⋮ Examples of finitely generated metabelian groups not residually finite with respect to conjugacy and occurrence, and representation of groups of the form \(F/R'\gamma_m(F) \) ⋮ The congruence subgroup problem for low rank free and free metabelian groups ⋮ Partially commutative metabelian groups: centralizers and elementary equivalence. ⋮ On nilpotent and metabelian products of groups. ⋮ Infinite groups ⋮ Relation modules of infinite groups. II. ⋮ Verbally closed subgroups of free solvable groups ⋮ Subgroup distortion in wreath products of cyclic groups. ⋮ FREE SOLVABLE P-ALGEBRAS ⋮ Group rings ⋮ Unrecognizability of some residual properties for free groups ⋮ Approximation properties of nilpotent interlacings of groups. ⋮ Automorphism groufs and subgroups of sl₂over division rings ⋮ IA-automorphism of certain two-generator torsion-free groups ⋮ On embedding of partially commutative metabelian groups to matrix groups ⋮ Generalized Magnus embeddings and some applications ⋮ Retracts and verbally closed subgroups with respect to relatively free soluble groups ⋮ The congruence subgroup problem for the free metabelian group on \(n\geq 4\) generators ⋮ IA-automorphisms of the free metabelian group of rank 3 ⋮ The Magnus representation in congruence modular varieties ⋮ Epimorphisms between the free groups in a variety of groups ⋮ The conjugacy problem in free solvable groups and wreath products of abelian groups is in \(\mathsf{TC}^0\) ⋮ General theory of groups ⋮ Model-theoretic and algorithmic questions in group theory ⋮ On a presentation of the automorphism group of a partially commutative metabelian group

Cites Work

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• Groups that are residually finite with respect to conjugacy
• Residual Properties of Infinite Soluble Groups
• The Conjugacy Problem in Wreath Products and Free Metabelian Groups
• Residual finiteness of a class of knot groups

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