On the relation between upper central quotients and lower central series of a group

DOI10.1090/S0002-9947-01-02812-4zbMath1032.20023MaRDI QIDQ2723473

Graham J. Ellis

Publication date: 5 July 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

finite \(p\)-groupsBaer invariantsSchur multiplierslower central seriesupper central quotientsnonabelian tensor products of groups

Mathematics Subject Classification ID

Extensions, wreath products, and other compositions of groups (20E22) Finite nilpotent groups, (p)-groups (20D15) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12) Central extensions and Schur multipliers (19C09)

Related Items

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Cites Work

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• Powerful \(p\)-groups. I: Finite groups.
• Some computations of non-Abelian tensor products of groups
• Group extensions, representations, and the Schur multiplicator
• Van Kampen theorems for diagrams of spaces
• Cohomologie et groupe de Steinberg rélatifs
• The Schur multiplier of a pair of groups
• Tensor products of prime-power groups
• On the nilpotent multipliers of a group
• On groups with a finite nilpotent upper central quotient
• The nonabelian tensor square of a \(2\)-generator \(p\)-group of class \(2\)
• Multiplicators and groups with finite central factor-groups
• Group derived functors
• Über den Multiplikator von \(p\)-Gruppen. (On the multiplicator of \(p\)-groups)
• Multiplicators of \(p\)-groups
• On the number of automorphisms of a finite group
• The Ganea Map for Nilpotent Groups
• A bound for the derived and Frattini subgroups of a prime-power group
• On the Computation of Certain Homotopical Functors
• Inequalities for Baer Invariants of Finite Groups
• Higher Schur-multiplicator of a Finite Abelian Group
• Commutator subgroups of finite p-groups
• Some Inequalities for the Multiplicator of a Finite Group
• Some Inequalities for the Multiplicator of a Finite Group. II
• Baer-Invariants of Algebras
• Representations of groups as quotient groups. II. Minimal central chains of a group