# commutator subgroup

commutator subgroup
The subgroup of a specified group generated by the larger groups commutators.

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• Commutator subgroup — In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.[1][2] The commutator subgroup is important because it is the smallest… …   Wikipedia

• Commutator — This article is about the mathematical concept. For the relation between canonical conjugate entities, see canonical commutation relation. For the type of electrical switch, see commutator (electric). In mathematics, the commutator gives an… …   Wikipedia

• Subgroup series — In mathematics, a subgroup series is a chain of subgroups: Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important… …   Wikipedia

• commutator length — noun a) The number of multiplicands needed, at a minimum, to express a given group element as a product of commutators. In , the commutator length of is two, since it equals but isnt a commutator. b) The supremum, over all elements of a given… …   Wiktionary

• commutator group — Math. the subgroup of a given group, which consists of all the commutators in the group. [1960 65] * * * …   Universalium

• commutator group — Math. the subgroup of a given group, which consists of all the commutators in the group. [1960 65] …   Useful english dictionary

• Characteristic subgroup — In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.[1][2] Because conjugation is an automorphism, every… …   Wikipedia

• Normal subgroup — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Fully characteristic subgroup — In mathematics, a subgroup of a group is fully characteristic (or fully invariant) if it is invariant under every endomorphism of the group. That is, any endomorphism of the group takes elements of the subgroup to elements of the subgroup.Every… …   Wikipedia

• derived subgroup — noun The subgroup of a specified group generated by the larger groups commutators. Syn: commutator subgroup, derived group …   Wiktionary