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Title: Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups (English)
Author: Everaert, Tomas
Author: Gran, Marino
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 42
Issue: 4
Year: 2006
Pages: 387-396
Summary lang: English
Category: math
Summary: In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of $n$-nilpotent groups and of $n$-solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties. (English)
Keyword: relative commutator
Keyword: nilpotent groups
Keyword: solvable groups
Keyword: central extensions
MSC: 20E10
MSC: 20F12
MSC: 20F14
idZBL: Zbl 1152.20030
idMR: MR2283019
Date available: 2008-06-06T22:48:51Z
Last updated: 2012-05-10
Stable URL:
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Reference: [2] Fröhlich A.: Baer-invariants of algebras.Trans. Amer. Math. Soc. 109 (1963), 221–244. Zbl 0122.25702, MR 0158920
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Reference: [4] Higgins P. J.: Groups with multiple operators.Proc. London Math. Soc. (1956), 366–416. Zbl 0073.01704, MR 0082492
Reference: [5] Janelidze G., Kelly G. M.: Galois theory and a general notion of central extension.J. Pure Appl. Algebra 97 (1994), 135–161. Zbl 0813.18001, MR 1312759
Reference: [6] Lue A. S.-T.: Baer-invariants and extensions relative to a variety.Proc. Camb. Phil. Soc. 63 (1967), 569–578. Zbl 0154.27501, MR 0217151


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