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Relative commutator theory in varieties of \(\Omega\)-groups. (English) Zbl 1117.08007

Summary: We introduce a new notion of commutator which depends on the choice of a subvariety in any variety of \(\Omega\)-groups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules.

MSC:

08B99 Varieties
20F12 Commutator calculus
20E22 Extensions, wreath products, and other compositions of groups
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