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- ...s 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 [362 bytes (57 words) - 20:28, 31 January 2009
- 89 bytes (13 words) - 13:22, 5 December 2008
- 201 bytes (27 words) - 11:59, 15 June 2009

## Page text matches

- ...s 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 [362 bytes (57 words) - 20:28, 31 January 2009
- Group of order 4; smallest non-cyclic group79 bytes (9 words) - 09:57, 30 July 2009
- ...ers occur naturally in number theory ([[residue set]]s and group theory ([[cyclic group]]s, [[permutation]]s).2 KB (361 words) - 21:13, 6 January 2011
- ...group of units|multiplicative group]] of the field, which is necessarily [[cyclic group|cyclic]].790 bytes (108 words) - 14:54, 27 October 2008
- {{r|Cyclic group}}307 bytes (40 words) - 11:59, 15 June 2009
- {{r|Cyclic group}}245 bytes (30 words) - 10:06, 12 July 2008
- ...een the two is that the order of an element is equal to the order of the [[cyclic group]] generated by that element.857 bytes (146 words) - 13:24, 1 February 2009
- {{r|Cyclic group}}1 KB (180 words) - 17:00, 11 January 2010
- ...abelian group|abelian]] [[p-group|''p''-group]] ''M'' is a direct sum of [[cyclic group|cyclic]] ''p''-power components2 KB (264 words) - 22:53, 19 February 2010
- ...math>\Phi: x \mapsto x^p</math>. The automorphism group in this case is [[cyclic group|cyclic]] of order ''f'', generated by <math>\Phi</math>.3 KB (418 words) - 12:18, 20 December 2008
- {{r|Cyclic group}}187 bytes (26 words) - 13:43, 5 January 2011
- # The [[cyclic group]] of order 4, which can be represented by addition [[modular arithmetic|mo |'''Model of the [[cyclic group]] of order 4.'''5 KB (819 words) - 10:52, 15 September 2009
- ...uppe''' (German, meaning group of four) is the smallest [[cyclic group|non-cyclic group]]. It is an [[Abelian group| Abelian (commutative) group]] of order 4.3 KB (395 words) - 11:25, 30 July 2009
- ...sual action of <math>S_n</math> on <math>X = \{1,\ldots,n\}</math>. The [[cyclic group|cyclic]] subgroup <math>\langle \pi \rangle</math> generated by <math>\pi</4 KB (727 words) - 12:37, 16 November 2008
- {{r|Cyclic group}}2 KB (247 words) - 17:28, 11 January 2010
- ...n'' has a primitive root if the [[multiplicative group]] modulo ''n'' is [[cyclic group|cyclic]], and the primitive root is a [[generator]], having an [[order (gro2 KB (338 words) - 16:43, 6 February 2009
- {{r|Cyclic group}}856 bytes (107 words) - 18:36, 11 January 2010
- ...set of all the integral powers of the element ''g'' and its inverse. Every cyclic group is abelian, but the converse is not true (see the examples). The [[integer]]s together with addition is a cyclic group. Consider the required properties:15 KB (2,535 words) - 20:29, 14 February 2010
- ...tion is the ''only'' infinite cyclic group, in the sense that any infinite cyclic group is [[group isomorphism|isomorphic]] to '''Z'''.10 KB (1,566 words) - 03:12, 14 February 2010
- ...l)|vectors]] in the plane, and the various [[finite groups]] such as the [[cyclic group]]s that are the group of integers [[modular arithmetic|modulo]] ''n''. [[Se18 KB (2,667 words) - 19:22, 20 August 2020