cyclic 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

• Cyclic group — Group theory Group theory …   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

• Subgroup growth — Im mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. [citebook|title=Subgroup Growth|author=Alexander Lubotzky, Dan Segal|year=2003|publisher=Birkhäuser|id=ISBN… …   Wikipedia

• Cyclic category — In mathematics, the cyclic category or cycle category or category of cycles is a category of finite cyclically ordered sets and degree 1 maps between them. It was introduced by Connes (1983). Contents 1 Definition 2 Properties 3 Cyclic sets …   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

• Locally cyclic group — In group theory, a locally cyclic group is a group ( G , *) in which every finitely generated subgroup is cyclic.ome facts*Every cyclic group is locally cyclic, and every locally cyclic group is abelian. *Every finitely generated locally cyclic… …   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

• Fundamental theorem of cyclic groups — In abstract algebra, the fundamental theorem of cyclic groups states that if G, is a cyclic group of order n, then every subgroup of G, is cyclic. Moreover, the order of any subgroup of G, is a divisor of n, and for each positive divisor k, of n …   Wikipedia

• Pure subgroup — In mathematics, especially in the area of algebra studying the theory of abelian groups, a pure subgroup is a generalization of direct summand. It has found many uses in abelian group theory and related areas.DefinitionA subgroup S of a… …   Wikipedia

• Omega and agemo subgroup — In mathematics, or more specifically group theory, the omega and agemo subgroups described the so called power structure of a finite p group. They were introduced in (Hall 1933) where they were used to describe a class of finite p groups whose… …   Wikipedia