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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.