| 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:
|
http://hdl.handle.net/10338.dmlcz/108014 |
| . |
| Reference:
|
[1] Everaert T.: Relative commutator theory in varieties of $\Omega $-groups.J. Pure Appl. Algebra (to appear), preprint arXiv.math. RA/0605305. Zbl 1117.08007, MR 2311168 |
| Reference:
|
[2] Fröhlich A.: Baer-invariants of algebras.Trans. Amer. Math. Soc. 109 (1963), 221–244. Zbl 0122.25702, MR 0158920 |
| Reference:
|
[3] Furtado-Coelho J.: Homology and generalized Baer invariants.J. Algebra 40 (1976), 596–609. Zbl 0372.20037, MR 0414740 |
| 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 |
| . |
