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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|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]] <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 \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 <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 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 <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 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 <math>G</math> 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]] <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 characteristic
    2 KB (373 words) - 03:51, 14 January 2014
  • | 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 <math>A</math> to be a cyclic group of order 2 and <math>C = S_3</math> (the [[particular example::symmetric gr
    2 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>. Le
    3 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 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 <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

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