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• Cyclic group
  ... morphic]] to the [[additive group]] of the [[integer]]s, or to an additive group with respect to a fixed [[modular arithmetic|modulus]].
  Relevance: 6.3% - 362 B (57 words) - 01:28, 1 February 2009
• Cyclic group/Definition
  A group consisting of the powers of a single element.
  Relevance: 5.0% - 89 B (13 words) - 18:22, 5 December 2008
• Cyclic group/Related Articles
  {{r|Abelian group}}
  Relevance: 4.3% - 201 B (27 words) - 16:59, 15 June 2009

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• Cyclic group
  ... morphic]] to the [[additive group]] of the [[integer]]s, or to an additive group with respect to a fixed [[modular arithmetic|modulus]].
  Relevance: 9.1% - 362 B (57 words) - 01:28, 1 February 2009
• Examples of groups
  ... simple and natural generalization of common phenomena, so '''examples of groups''' are easily found, from all areas of mathematics. ==Different classes of groups==
  Relevance: 7.4% - 5 KB (819 words) - 13:00, 8 June 2009
• Group theory
  In mathematics, '''groups''' often arise as structures representing the set of possible symmetries ... ... bined, and the full group of symmetries is called the 2-dimensional affine group. [[Felix Klein]] pioneered this approach to geometry, calling it the [[Erl ...
  Relevance: 6.3% - 15 KB (2535 words) - 02:26, 14 February 2009
• Integer
  ... '' infinite cyclic group, in the sense that any infinite cyclic group is [[group isomorphism|isomorphic]] to '''Z'''. ... ht hand side is odd. This means that '''Z''' under multiplication is not a group.
  Relevance: 5.2% - 10 KB (1566 words) - 15:40, 8 December 2008
• Primitive element
  ... s|multiplicative group]] of the field, which is necessarily [[cyclic group|cyclic]].
  Relevance: 5.0% - 790 B (108 words) - 19:54, 27 October 2008
• Primitive root/Definition
  ... rator of the multiplicative group in modular arithmetic when that group is cyclic.
  Relevance: 4.9% - 124 B (17 words) - 07:36, 5 December 2008
• Abelian group/Related Articles
  {{r|Group (mathematics)}} {{r|Cyclic group}}
  Relevance: 4.9% - 245 B (30 words) - 15:06, 12 July 2008
• Field automorphism
  ... iven field ''K'' form a [[group (mathematics)|group]], the '''automorphism group''' <math>Aut(K)</math>. ... s ''[[normal extension|normal]]'' if the automorphism group is of [[order (group theory)|order]] equal to ''d''.
  Relevance: 4.9% - 3 KB (418 words) - 17:18, 20 December 2008
• Hall polynomial
  ... ematics]] were developed by [[Philip Hall]] in the 1950s in the study of [[group representation]]s. ... |abelian]] [[p-group|''p''-group]] ''M'' is a direct sum of [[cyclic group|cyclic]] ''p''-power components
  Relevance: 4.8% - 2 KB (270 words) - 18:45, 8 March 2009
• Primitive root
  ... up|cyclic]], and the primitive root is a [[generator]], having an [[order (group theory)|order]] equal to [[Euler's totient function]] φ(''n''). Another ...
  Relevance: 4.6% - 2 KB (338 words) - 21:43, 6 February 2009
• Discrete logarithm/Related Articles
  {{r|Group homomorphism}} <!-- more precisely, group isomorphism --> {{r|Cyclic group}}
  Relevance: 3.4% - 307 B (40 words) - 16:59, 15 June 2009
• Algebra
  ... their precise definitions lead to structures such as [[group (mathematics)|groups]], [[ring (mathematics)|rings]] and [[field (mathematics)|fields]]. ... algebra'', in which [[algebraic structure]]s such as [[group (mathematics)|groups]], [[ring (mathematics)|rings]] and [[field theory (mathematics)|field]]s ...
  Relevance: 2.3% - 27 KB (3906 words) - 07:53, 13 December 2008
• Order (group theory)
  ... at raising the element to that power gives the [[identity element]] of the group. If there is no such number, the element is said to be of ''infinite orde ... ... two is that the order of an element is equal to the order of the [[cyclic group]] generated by that element.
  Relevance: 2.2% - 857 B (146 words) - 18:24, 1 February 2009
• Group action
  ... tics]], a '''group action''' is a relation between a [[group (mathematics)|group]] ''G'' and a [[set (mathematics)|set]] ''X'' in which the elements of ''G ... Formally, a group action is a map from the [[Cartesian product]] <math>G \times X \rightarro ...
  Relevance: 2.2% - 4 KB (727 words) - 17:37, 16 November 2008
• Glucose
  ... Depending on the stereochemical orientation of the resulting C-1 hydroxyl group formed in this reaction, the products are labeled as alpha or beta (see il ...
  Relevance: 1.4% - 1 KB (200 words) - 13:08, 8 June 2009
• Quadratic field
  ===Unit group=== ... gers are [[root of unity|roots of unity]]. If ''d'' is positive, the unit group has rank one, with a [[fundamental unit]] of infinite order.
  Relevance: 1.2% - 3 KB (453 words) - 22:18, 6 February 2009
• Polynomial/Advanced
  ... f the [[monoid]] of non-negative powers of the generator ''X'' of a cyclic group. This method also allows one to define non-commuting polynomial rings, an ...
  Relevance: 1.0% - 10 KB (1741 words) - 15:04, 3 January 2009
• Cyclic GMP
  ... stry]], '''cyclic GMP''' is a "guanine nucleotide containing one phosphate group which is esterified to the sugar moiety in both the 3'- and 5'-positions. ...
  Relevance: 1.0% - 523 B (75 words) - 01:18, 16 July 2008
• Bacterial cell structure
  The smallest bacteria include a subgroup of marine [[Alphaproteobacteria]] which comprise up to 25 percent of the o ... ... %G+C Gram positive organisms). Bacteria within the [[Deinococcus-Thermus]] group may also exhibit Gram positive staining behaviour but contain some cell wa ...
  Relevance: 0.9% - 22 KB (3294 words) - 08:11, 8 June 2009
• Adenosine
  ... ine is bound to two hydrogen atoms rather than one proton and one hydroxyl group. Adenosine inhibits the effects intracellular [[cyclic AMP]] thus reducing [[sympathetic nervous system|sympathetic]] stimulation ...
  Relevance: 0.8% - 2 KB (286 words) - 02:48, 16 July 2008

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