Some applications of free differential calculus in group theory

DOI10.1007/BF01158317zbMath0733.20014OpenAlexW2051383098MaRDI QIDQ810145

V. Eh. Shpil'rajn

Publication date: 1991

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01158317

zbMATH Keywords

exponentfree groupdifferential calculuslower central seriestorsion groupresidually nilpotentaugmentation idealisolatordiscriminated by nilpotent groupsfree abelianfreely generatedgeneralized Fox derivativeshopfianright Fox derivatives

Mathematics Subject Classification ID

Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Fundamental group, presentations, free differential calculus (57M05) Free nonabelian groups (20E05) Residual properties and generalizations; residually finite groups (20E26) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12)

Cites Work

• On torsion in free central extensions of some torsion-free groups
• On Gupta representations of central extensions
• Magnus embeddings and residual nilpotence
• Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
• The Hopficity of F/r′

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