Relative commutator associated with varieties of n -nilpotent and of n -solvable groups

Tomas Everaert; Marino Gran

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 4, page 387-396
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Everaert, Tomas, and Gran, Marino. "Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups." Archivum Mathematicum 042.4 (2006): 387-396. <http://eudml.org/doc/249776>.

@article{Everaert2006,
abstract = {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.},
author = {Everaert, Tomas, Gran, Marino},
journal = {Archivum Mathematicum},
keywords = {relative commutator; nilpotent groups; solvable groups; central extensions; relative commutators; nilpotent groups; solvable groups; central extensions},
language = {eng},
number = {4},
pages = {387-396},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups},
url = {http://eudml.org/doc/249776},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Everaert, Tomas
AU - Gran, Marino
TI - Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 4
SP - 387
EP - 396
AB - 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.
LA - eng
KW - relative commutator; nilpotent groups; solvable groups; central extensions; relative commutators; nilpotent groups; solvable groups; central extensions
UR - http://eudml.org/doc/249776
ER -

References

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  1. Everaert T., Relative commutator theory in varieties of Ω -groups, J. Pure Appl. Algebra (to appear), preprint arXiv.math. RA/0605305. Zbl1117.08007MR2311168
  2. Fröhlich A., Baer-invariants of algebras, Trans. Amer. Math. Soc. 109 (1963), 221–244. (1963) Zbl0122.25702MR0158920
  3. Furtado-Coelho J., Homology and generalized Baer invariants, J. Algebra 40 (1976), 596–609. (1976) Zbl0372.20037MR0414740
  4. Higgins P. J., Groups with multiple operators, Proc. London Math. Soc. (1956), 366–416. (1956) Zbl0073.01704MR0082492
  5. Janelidze G., Kelly G. M., Galois theory and a general notion of central extension, J. Pure Appl. Algebra 97 (1994), 135–161. (1994) Zbl0813.18001MR1312759
  6. Lue A. S.-T., Baer-invariants and extensions relative to a variety, Proc. Camb. Phil. Soc. 63 (1967), 569–578. (1967) Zbl0154.27501MR0217151

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