Cyclic group: Difference between revisions
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imported>Richard Pinch (new entry, just a placeholder really) |
imported>Howard C. Berkowitz No edit summary |
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In [[group theory]], a '''cyclic group''' is a [[group]] with a single generator. The elements of the group are then just the powers of this generating element. Every cyclic group is thus [[group isomorphism|isomorphic]] to the [[additive group]] of the [[integer]]s, or to an additive group with respect to a fixed [[modular arithmetic|modulus]]. | In [[group theory]], a '''cyclic group''' is a [[group]] with a single generator. The elements of the group are then just the powers of this generating element. Every cyclic group is thus [[group isomorphism|isomorphic]] to the [[additive group]] of the [[integer]]s, or to an additive group with respect to a fixed [[modular arithmetic|modulus]]. | ||
Latest revision as of 20:28, 31 January 2009
In group theory, a cyclic group is a group with a single generator. The elements of the group are then just the powers of this generating element. Every cyclic group is thus isomorphic to the additive group of the integers, or to an additive group with respect to a fixed modulus.