# Search results

## Page title matches

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

## Page text matches

- ...morphic]] to the [[additive group]] of the [[integer]]s, or to an additive group with respect to a fixed [[modular arithmetic|modulus]].362 B (57 words) - 01:28, 1 February 2009
- ...simple and natural generalization of common phenomena, so '''examples of groups''' are easily found, from all areas of mathematics. ==Different classes of groups==5 KB (819 words) - 15:52, 15 September 2009
- ...group|non-cyclic group]]. It is an [[Abelian group| Abelian (commutative) group]] of order 4. The group was given his name by [[Felix Klein]] in his 1884 lectures "''Vorlesungen3 KB (395 words) - 16:25, 30 July 2009
- In mathematics, '''groups''' often arise as structures representing the set of possible symmetries o ...bined, and the full group of symmetries is called the 2-dimensional affine group. [[Felix Klein]] pioneered this approach to geometry, calling it the [[Erla15 KB (2,535 words) - 01:29, 15 February 2010
- ...'' 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.10 KB (1,566 words) - 08:12, 14 February 2010
- Group of order 4; smallest non-cyclic group79 B (9 words) - 14:57, 30 July 2009
- ...s|multiplicative group]] of the field, which is necessarily [[cyclic group|cyclic]].790 B (108 words) - 19:54, 27 October 2008
- ...rator of the multiplicative group in modular arithmetic when that group is cyclic.124 B (17 words) - 07:36, 5 December 2008
- ...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 components2 KB (264 words) - 03:53, 20 February 2010
- {{r|Group (mathematics)}} {{r|Cyclic group}}245 B (30 words) - 15:06, 12 July 2008
- ...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''.3 KB (418 words) - 17:18, 20 December 2008
- ...up|cyclic]], and the primitive root is a [[generator]], having an [[order (group theory)|order]] equal to [[Euler's totient function]] φ(''n''). Another w2 KB (338 words) - 21:43, 6 February 2009
- {{r|Group homomorphism}} <!-- more precisely, group isomorphism --> {{r|Cyclic group}}307 B (40 words) - 16:59, 15 June 2009
- Auto-populated based on [[Special:WhatLinksHere/Group theory]]. Needs checking by a human. {{r|Baer-Specker group}}1 KB (180 words) - 22:00, 11 January 2010
- The typical example of a '''cyclic order''' are people seated at a (round) table: This gives rise to a cyclic order if (and only if) for some element ''s'' the orbit under σ is th2 KB (361 words) - 02:13, 7 January 2011
- {{r|Cyclic group}}187 B (26 words) - 18:43, 5 January 2011
- ...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]]s18 KB (2,667 words) - 00:22, 21 August 2020
- ...utes a realisation of the cocycles in the second [[cohomology group]] in [[group cohomology]]. Let ''G'' be a group and ''L'' a field on which ''G'' acts as automorphisms. A ''cocycle'' or '3 KB (519 words) - 20:42, 2 January 2013
- ...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 order ...two is that the order of an element is equal to the order of the [[cyclic group]] generated by that element.857 B (146 words) - 18:24, 1 February 2009
- ...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 \rightarrow4 KB (727 words) - 17:37, 16 November 2008