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Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups
Archivum mathematicum, Tome 42 (2006) no. 4, pp. 387-396
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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.
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 
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     title = {Relative commutator associated with varieties of $n$-nilpotent and of $n$-solvable groups},
     journal = {Archivum mathematicum},
     pages = {387--396},
     year = {2006},
     volume = {42},
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     zbl = {1152.20030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2006_42_4_a3/}
}
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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/

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