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.
@article{108014,
author = {Tomas Everaert and Marino Gran},
title = {Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {387-396},
zbl = {1152.20030},
mrnumber = {2283019},
language = {en},
url = {http://dml.mathdoc.fr/item/108014}
}
Everaert, Tomas; Gran, Marino. Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups. Archivum Mathematicum, Tome 042 (2006) pp. 387-396. http://gdmltest.u-ga.fr/item/108014/
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