Relative Commutator Theory in Varieties of Ω-groups
نویسنده
چکیده
We introduce a new notion of commutator which depends on a choice of subvariety in any variety of Ω-groups. We prove that this notion encompasses Higgins’s commutator, Fröhlich’s central extensions and the Peiffer commutator of precrossed modules.
منابع مشابه
RELATIVE COMMUTATOR ASSOCIATED WITH VARIETIES OF n-NILPOTENT AND OF n-SOLVABLE GROUPS
A new notion of commutator was defined in any variety of Ω-groups A, relative to any fixed subvariety B of A [1]. This notion gives back the usual commutator of normal subgroups when A is the variety of groups and B the subvariety of abelian groups (see Section 2), but also the Peiffer commutator of normal precrossed submodules, when A is the variety of precrossed modules and B the subvariety o...
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