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- ..., inverse and the identity element. Typically, when talking of a black-box cyclic group, one additional piece of information is furnished: the [[order of a group|o899 bytes (136 words) - 21:08, 25 June 2013
- {{further|[[Equivalence of definitions of cyclic group]]}} See [[finite cyclic group#Arithmetic functions]] and [[group of integers#Arithmetic functions]].8 KB (1,111 words) - 23:25, 20 June 2013
- 27 bytes (3 words) - 23:25, 7 May 2008
- The cyclic group of order 2 is defined as the unique group of order two. Explicitly it can b | [[satisfies property::cyclic group]] || Yes ||8 KB (1,234 words) - 05:31, 21 January 2013
- The cyclic group of order 3 is defined as the unique group of order 3. Equivalently it can b ...s property::Cyclic group]] || Yes || By definition || Smallest [[odd-order cyclic group]]6 KB (839 words) - 04:07, 12 January 2013
- group = cyclic group:Z4| Note that since the group is a [[cyclic group]], all subgroups are [[characteristic subgroup]]s (see [[cyclic implies eve2 KB (188 words) - 01:56, 1 July 2011
- group = cyclic group:Z2| | [[finite cyclic group]] || 2 || [[Family version::linear representation theory of finite cyclic g5 KB (709 words) - 02:18, 5 December 2011
- group = cyclic group:Z3| This article discusses the linear representation theory of [[cyclic group:Z3]], a group of order three.9 KB (1,313 words) - 23:09, 9 May 2011
- ...lomorph of a group|holomorph]] of the [[cyclic group of prime-square order|cyclic group of order]] <math>p^2</math>. ...[[semidirect product]] of the cyclic group <math>\Z/p^2\Z</math> with the cyclic group <math>\Z/p\Z</math>, where <math>a \in \Z/p\Z</math> acts on <math>x \in \Z7 KB (1,015 words) - 17:22, 3 May 2015
- ...'topologically monogenic''' if there exists a [[tps:dense subset|dense]] [[cyclic group|cyclic]] [[subgroup]]. Any [[cyclic group]] is topologically cyclic, irrespective of the topology.445 bytes (51 words) - 18:01, 2 August 2012
- ...p''' to describe <math>H</math> in <math>G</matH> if <math>G</math> is a [[cyclic group]]. ...roup of itself)|| {{intermediate notions short|verbal subgroup|subgroup of cyclic group}}2 KB (269 words) - 02:29, 16 February 2013
- 31 bytes (4 words) - 19:09, 30 July 2008
- #redirect [[Cyclic group:Z2]]29 bytes (4 words) - 12:00, 25 May 2008
- #redirect [[Cyclic group:Z2]]29 bytes (4 words) - 12:37, 25 May 2008
- #redirect [[Cyclic group:Z3]]29 bytes (4 words) - 12:38, 25 May 2008
- #redirect [[Cyclic group:Z3]]29 bytes (4 words) - 12:39, 25 May 2008
- 34 bytes (5 words) - 15:54, 17 June 2008
- This article describes various actions of the cyclic group of order two on topological spaces. Two actions of a group on a topological ...ed points. More specifically, a properly discontinuous group action of the cyclic group of order two is equivalent to a fixed-point free self-homeomorphism of the5 KB (757 words) - 21:51, 14 April 2009
- {{definition equivalence|cyclic group}}4 KB (649 words) - 16:48, 8 December 2008
- ...the exponent is reduced modulo <math>4</math>. In other words, it is the [[cyclic group]] whose [[order of a group|order]] is four. It can also be viewed as: |[[Satisfies property::Cyclic group]] || Yes || By definition || Smallest cyclic group of composite order4 KB (464 words) - 01:42, 5 December 2011
Page text matches
- subgroup = cyclic group:Z2|1 KB (187 words) - 22:11, 28 June 2011
- | 2 || 2 || [[cyclic group:Z2]] || -- ...automorphism group. In other words, the [[outer automorphism group]] is [[cyclic group:Z2]]. See [[automorphism group of symmetric group:S6]].4 KB (564 words) - 17:24, 1 October 2011
- ...3]], i.e., the alternating group of degree three, which is isomorphic to [[cyclic group:Z3]] (these are the ''even'' permutations). The non-identity coset of this21 KB (2,660 words) - 01:57, 23 February 2014
- The sole effect of this command is to output the [[cyclic group]] of order 23. The group isn't output as a multiplication table; rather a s outputs the cyclic group of order 23, and also stores the information that <math>G</math> equals thi7 KB (1,180 words) - 22:24, 7 May 2008
- #redirect [[cyclic group:Z3]]29 bytes (4 words) - 01:35, 5 December 2011
- ..., inverse and the identity element. Typically, when talking of a black-box cyclic group, one additional piece of information is furnished: the [[order of a group|o899 bytes (136 words) - 21:08, 25 June 2013
- ...up of the [[finite field]] <math>\mathbb{F}_p</math>) is isomorphic to the cyclic group of order <math>p-1</math>.2 KB (408 words) - 07:21, 21 December 2014
- # If two permutation representations of a [[cyclic group]] are conjugate in the general linear group over a field of characteristic2 KB (373 words) - 03:51, 14 January 2014
- | 2 || 1 || [[cyclic group:Z2]] || 2 || 1 | 3 || 1 || [[cyclic group:Z3]] || 3 || 14 KB (586 words) - 05:01, 11 April 2017
- A [[group]] is termed a '''C1-group''' if every [[cyclic group|cyclic]] [[subgroup]] is [[self-conjugate-permutable subgroup|self-conjugat541 bytes (61 words) - 23:12, 7 May 2008
- ...oup''' or a ''cyclic subgroups are conjugate-permutable'' group if every [[cyclic group|cyclic]] subgroup is [[conjugate-permutable subgroup|conjugate-permutable]]799 bytes (99 words) - 23:12, 7 May 2008
- * A nontrivial [[cyclic group]] cannot be capable. This is because there cannot be an element ''outside''3 KB (351 words) - 19:19, 12 January 2013
- ...obtained from the generic example above by setting <math>A</math> to be a cyclic group of order 2 and <math>C = S_3</math> (the [[particular example::symmetric gr2 KB (238 words) - 20:04, 1 June 2016
- and <math>C</math> is the [[cyclic group:Z2|cyclic group on two elements]], with generator <math>y</math>.2 KB (265 words) - 23:24, 15 February 2009
- Consider the cyclic group <math>\mathbb{Z}/p\mathbb{Z}</math> which we denote as <math>C_p</math>. Le3 KB (403 words) - 23:14, 7 May 2008
- {{further|[[Particular example::cyclic group:Z3]]}} Let <math>G</math> be the cyclic group of order three and <math>\R</math> be the field. <math>G</math> has an irre7 KB (1,135 words) - 17:46, 1 June 2016
- ...he core is trivial while for others it is nontrivial. For instance, in the cyclic group of that order, the core is the whole Sylow subgroup, whereas if there is a2 KB (287 words) - 23:24, 7 May 2008
- ...oup of degree <math>l</math> (order <math>2l</math>) and [[cyclic group:Z2|cyclic group of order two]]4 KB (551 words) - 07:22, 15 May 2015
- ...group]] is said to be a '''cyclic-center group''' if its [[center]] is a [[cyclic group]]. * [[Cyclic group]]510 bytes (68 words) - 23:24, 7 May 2008
- ...lic characteristic subgroup]] such that the [[quotient group]] is also a [[cyclic group]]. * [[Weaker than::Cyclic group]]669 bytes (72 words) - 16:39, 14 February 2009
