- trivial subgroup
- мат. тривиальная подгруппа
Большой англо-русский и русско-английский словарь. 2001.
trivial subgroup
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Subgroup — This article is about the mathematical concept For the galaxy related concept, see Galaxy subgroup. Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum … Wikipedia
Trivial group — In mathematics, a trivial group is a group consisting of a single element. All such groups are isomorphic so one often speaks of the trivial group. The single element of the trivial group, variously labeled e , 1, or 0, is the identity element.… … 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
trivial — adjective 1》 of little value or importance. 2》 Mathematics denoting a subgroup that either contains only the identity element or is identical with the given group. Derivatives triviality noun (plural trivialities). trivially adverb Word History… … English new terms dictionary
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
Essential subgroup — In mathematics, especially in the area of algebra studying the theory of abelian groups, an essential subgroup is a subgroup that determines much of the structure of its containing group. The concept was generalized to essential… … 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
Malnormal subgroup — In mathematics, in the field of group theory, a subgroup H of a group G is termed malnormal if for any x in G but not in H, H and Hx intersect in the identity element. Some facts about malnormality: An intersection of malnormal subgroups is… … Wikipedia
Centrally closed subgroup — In mathematics, in the realm of group theory, a subgroup of a group is said to be centrally closed if the centralizer of any nonidentity element of the subgroup lies inside the subgroup.Some facts about centrally closed subgroups:* Every… … 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
Kurosh subgroup theorem — In the mathematical field of group theory, the Kurosh subgroup theorem descibes the algebraic structure of subgroups of free products of groups. The theorem was obtained by a Russian mathematician Alexander Kurosh in 1934. [A. G. Kurosh, Die… … Wikipedia
