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Keywords:
relative commutator; nilpotent groups; solvable groups; central extensions
relative commutator; nilpotent groups; solvable groups; central extensions
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.
References:
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