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## Page title matches

• ..., 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|o
899 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 eve
2 KB (188 words) - 01:56, 1 July 2011
• group = cyclic group:Z2| | [[finite cyclic group]] || 2 || [[Family version::linear representation theory of finite cyclic g
5 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]] $p^2$. ...[[semidirect product]] of the cyclic group $\Z/p^2\Z$ with the cyclic group $\Z/p\Z$, where $a \in \Z/p\Z$ acts on $x \in \Z 7 KB (1,015 words) - 17:22, 3 May 2015 • ...'topologically monogenic''' if there exists a [[tps:dense subset|dense]] [[cyclic group|cyclic]] [[subgroup]]. Any [[cyclic group]] is topologically cyclic, irrespective of the topology. 445 bytes (51 words) - 18:01, 2 August 2012 • ...p''' to describe [itex]H$ in $G</matH> if [itex]G$ 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 the
5 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 $4$. 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 order
4 KB (491 words) - 22:44, 5 July 2019

## 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 this
21 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 $G$ equals thi
7 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|o
899 bytes (136 words) - 21:08, 25 June 2013
• ...up of the [[finite field]] $\mathbb{F}_p$) is isomorphic to the cyclic group of order $p-1$.
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 characteristic
2 KB (377 words) - 20:33, 28 September 2021
• | 2 || 1 || [[cyclic group:Z2]] || 2 || 1 | 3 || 1 || [[cyclic group:Z3]] || 3 || 1
4 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-conjugat
541 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 $A$ to be a cyclic group of order 2 and $C = S_3$ (the [[particular example::symmetric gr
2 KB (238 words) - 20:04, 1 June 2016
• and $C$ is the [[cyclic group:Z2|cyclic group on two elements]], with generator $y$.
2 KB (265 words) - 23:24, 15 February 2009
• Consider the cyclic group $\mathbb{Z}/p\mathbb{Z}$ which we denote as $C_p$. Le
3 KB (403 words) - 23:14, 7 May 2008
• {{further|[[Particular example::cyclic group:Z3]]}} Let $G$ be the cyclic group of order three and $\R$ be the field. $G$ has an irre
7 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 a
2 KB (287 words) - 23:24, 7 May 2008
• ...oup of degree $l$ (order $2l$) 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

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