One-relator groups and the lower central series. I: The splitting isomorphism

DOI10.1016/0022-4049(82)90012-3zbMath0467.20030OpenAlexW2045827554MaRDI QIDQ1155720

Kathy Horadam

Publication date: 1982

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(82)90012-3

zbMATH Keywords

Lie ringone-relator groupsisomorphism problemstandard commutator

Mathematics Subject Classification ID

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) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Associated Lie structures for groups (20F40)

Related Items (1)

One-relator groups and the lower central series. II: Invariants of one- relator groups

Cites Work

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• The diagonal comultiplication on homology
• The isomorphism problem for a class of one-relator groups
• On the descending central series of groups with a single defining relation
• The isomorphism problem for one-relator groups with non-trivial centre
• A Quick Test for Nonisomorphism of One-Relator Groups
• The Isomorphism Problem for Two-Generator One-Relator Groups with Torsion is Solvable
• Free differential calculus. IV: The quotient groups of the lower central series

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