Geodesic
Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups
Archivum mathematicum, Tome 42 (2006) no. 4, pp. 387-396 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 20E10, 20F12, 20F14
Keywords: relative commutator; nilpotent groups; solvable groups; central extensions 
@article{ARM_2006_42_4_a3,
     author = {Everaert, Tomas and Gran, Marino},
     title = {Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups},
     journal = {Archivum mathematicum},
     pages = {387--396},
     year = {2006},
     volume = {42},
     number = {4},
     mrnumber = {2283019},
     zbl = {1152.20030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a3/}
}
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
SP  - 387
EP  - 396
VL  - 42
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a3/
LA  - en
ID  - ARM_2006_42_4_a3
ER  - 
%0 Journal Article
%A Everaert, Tomas
%A Gran, Marino
%T Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups
%J Archivum mathematicum
%D 2006
%P 387-396
%V 42
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a3/
%G en
%F ARM_2006_42_4_a3
Everaert, Tomas; Gran, Marino. Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups. Archivum mathematicum, Tome 42 (2006) no. 4, pp. 387-396. http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a3/

[1] Everaert T.: Relative commutator theory in varieties of $\Omega $-groups. J. Pure Appl. Algebra (to appear), preprint arXiv.math. RA/0605305. | MR | Zbl

[2] Fröhlich A.: Baer-invariants of algebras. Trans. Amer. Math. Soc. 109 (1963), 221–244. | MR | Zbl

[3] Furtado-Coelho J.: Homology and generalized Baer invariants. J. Algebra 40 (1976), 596–609. | MR | Zbl

[4] Higgins P. J.: Groups with multiple operators. Proc. London Math. Soc. (1956), 366–416. | MR | Zbl

[5] Janelidze G., Kelly G. M.: Galois theory and a general notion of central extension. J. Pure Appl. Algebra 97 (1994), 135–161. | MR | Zbl

[6] Lue A. S.-T.: Baer-invariants and extensions relative to a variety. Proc. Camb. Phil. Soc. 63 (1967), 569–578. | MR | Zbl