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- Cyclic_group abstract "In algebra, a cyclic group is a group that is generated by a single element. That is, it consists of a set of elements with a single invertible associative operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation or its inverse to g. Each element can be written as a power of g in multiplicative notation, or as a multiple of g in additive notation. This element g is called a generator of the group.Every infinite cyclic group is isomorphic to the additive group of Z, the integers. Every finite cyclic group of order n is isomorphic to the additive group of Z/nZ, the integers modulo n. Every cyclic group is an abelian group (meaning that its group operation is commutative), and every finitely generated abelian group is a direct product of cyclic groups.".
- Cyclic_group thumbnail Cyclic_group.svg?width=300.
- Cyclic_group wikiPageExternalLink cyclic.html.
- Cyclic_group wikiPageExternalLink gt.html.
- Cyclic_group wikiPageID "52327".
- Cyclic_group wikiPageRevisionID "603483188".
- Cyclic_group hasPhotoCollection Cyclic_group.
- Cyclic_group subject Category:Abelian_group_theory.
- Cyclic_group subject Category:Finite_groups.
- Cyclic_group subject Category:Properties_of_groups.
- Cyclic_group type Abstraction100002137.
- Cyclic_group type FiniteGroups.
- Cyclic_group type Group100031264.
- Cyclic_group type Possession100032613.
- Cyclic_group type PropertiesOfGroups.
- Cyclic_group type Property113244109.
- Cyclic_group type Relation100031921.
- Cyclic_group comment "In algebra, a cyclic group is a group that is generated by a single element. That is, it consists of a set of elements with a single invertible associative operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation or its inverse to g. Each element can be written as a power of g in multiplicative notation, or as a multiple of g in additive notation.".
- Cyclic_group label "Cyclic group".
- Cyclic_group label "Cyclische groep".
- Cyclic_group label "Groupe cyclique".
- Cyclic_group label "Grupa cykliczna".
- Cyclic_group label "Grupo cíclico".
- Cyclic_group label "Grupo cíclico".
- Cyclic_group label "Gruppo ciclico".
- Cyclic_group label "Zyklische Gruppe".
- Cyclic_group label "Циклическая группа".
- Cyclic_group label "زمرة دائرية".
- Cyclic_group label "巡回群".
- Cyclic_group label "循環群".
- Cyclic_group sameAs Cyklická_grupa.
- Cyclic_group sameAs Zyklische_Gruppe.
- Cyclic_group sameAs Grupo_cíclico.
- Cyclic_group sameAs Groupe_cyclique.
- Cyclic_group sameAs Gruppo_ciclico.
- Cyclic_group sameAs 巡回群.
- Cyclic_group sameAs 순환군.
- Cyclic_group sameAs Cyclische_groep.
- Cyclic_group sameAs Grupa_cykliczna.
- Cyclic_group sameAs Grupo_cíclico.
- Cyclic_group sameAs m.0drq5.
- Cyclic_group sameAs Q245462.
- Cyclic_group sameAs Q245462.
- Cyclic_group sameAs Cyclic_group.
- Cyclic_group wasDerivedFrom Cyclic_group?oldid=603483188.
- Cyclic_group depiction Cyclic_group.svg.
- Cyclic_group isPrimaryTopicOf Cyclic_group.