cyclic group

Noun

Meaning

cyclic group (plural cyclic groups)

(group theory) A group generated by a single element.

Synonyms

Related terms

Examples

Any group of prime order is isomorphic to a cyclic group and therefore abelian. Source: Internet

Associated objects Representations The representation theory of the cyclic group is a critical base case for the representation theory of more general finite groups. Source: Internet

Denote the cyclic group of order p as W(1), and the wreath product of W(n) with W(1) as W(n + 1). Source: Internet

Every cyclic group can be given a structure as a cyclically ordered group, consistent with the ordering of the integers (or the integers modulo the order of the group). Source: Internet

Every cyclic group is virtually cyclic, as is every finite group. Source: Internet

Every infinite cyclic group is isomorphic to the additive group of Z, the integers. Source: Internet

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