- derived subgroup
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The subgroup of a specified group generated by the larger groups commutators.
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derived subgroup
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derived group — noun The subgroup of a specified group generated by the larger groups commutators. Syn: commutator subgroup, derived subgroup … Wiktionary
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
Derived functor — In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… … Wikipedia
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
Focal subgroup theorem — In abstract algebra, the focal subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in (Higman 1958) and is the first major application of the transfer according to… … Wikipedia
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
Fitting subgroup — In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G , named after Hans Fitting, is the unique largest normal nilpotent subgroup of G . Intuitively, it represents the smallest… … Wikipedia
commutator subgroup — noun The subgroup of a specified group generated by the larger groups commutators. Syn: derived group, derived subgroup … Wiktionary
Regular p-group — In mathematics, especially in the field of group theory, the concept of regular p group captures some of the more important properties of abelian p groups, but is general enough to include most small p groups. The concept was first described by… … Wikipedia
