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- == History of group theory == ...are not solvable. This is one of the first important results to arise from group theory. The fact that <math>S_5</math> is not solvable gives a proof that there is15 KB (2,535 words) - 20:29, 14 February 2010
- 12 bytes (1 word) - 16:02, 26 September 2007
- 121 bytes (15 words) - 08:25, 4 September 2009
- #REDIRECT [[Order (group theory)]]34 bytes (4 words) - 17:56, 21 November 2008
- ...m Magnus | coauthors=Abraham Karrass, Donald Solitar | title=Combinatorial Group Theory | edition=2nd revised edition | publisher=[[Dover Publications]] | date=1971 KB (137 words) - 02:15, 29 November 2008
- In [[group theory]], a '''character''' may refer one of two related concepts: a [[group homom680 bytes (98 words) - 06:19, 15 June 2009
- In [[group theory]], a '''series''' is a [[chain (mathematics)]] of [[subgroup]]s of a [[grou1 KB (198 words) - 17:19, 6 December 2008
- 31 bytes (5 words) - 12:35, 8 November 2008
- In [[group theory]], the '''order''' of a [[group (mathematics)|group]] element is the least857 bytes (146 words) - 13:24, 1 February 2009
- In [[group theory]], '''conjugation''' is an operation between group elements. The '''conjug2 KB (294 words) - 04:53, 19 November 2008
- Auto-populated based on [[Special:WhatLinksHere/Group theory]]. Needs checking by a human. {{r|Character (group theory)}}1 KB (180 words) - 17:00, 11 January 2010
- 199 bytes (32 words) - 17:17, 20 November 2008
- 110 bytes (15 words) - 06:26, 4 September 2009
- 297 bytes (38 words) - 17:41, 20 November 2008
- 901 bytes (116 words) - 19:33, 1 March 2008
- #REDIRECT [[Bona fide group theory]]36 bytes (5 words) - 19:33, 1 March 2008
- 105 bytes (15 words) - 17:22, 6 December 2008
- 140 bytes (20 words) - 19:59, 7 February 2009
- 141 bytes (19 words) - 23:06, 14 September 2009
- 12 bytes (1 word) - 21:06, 21 December 2007
- 12 bytes (1 word) - 18:38, 3 March 2008
- {{r|Group theory}}885 bytes (141 words) - 12:30, 29 December 2008
- 783 bytes (116 words) - 03:00, 7 November 2008
- {{r|Group theory}}294 bytes (36 words) - 06:17, 15 June 2009
- Auto-populated based on [[Special:WhatLinksHere/Order (group theory)]]. Needs checking by a human.594 bytes (76 words) - 19:15, 11 January 2010
Page text matches
- Auto-populated based on [[Special:WhatLinksHere/Group theory]]. Needs checking by a human. {{r|Character (group theory)}}1 KB (180 words) - 17:00, 11 January 2010
- {{r|Group theory}}654 bytes (81 words) - 13:36, 29 November 2008
- In [[group theory]], a '''cyclic group''' is a [[group]] with a single generator. The elemen362 bytes (57 words) - 20:28, 31 January 2009
- * [[Glossary of group theory]] * [[Elementary group theory]]890 bytes (130 words) - 11:11, 13 February 2009
- In [[group theory]], the '''centre of a group''' is the subset of elements which [[commutativ ...tic]]. It may be described as the set of elements by which [[conjugation (group theory)|conjugation]] is trivial (the identity map); this shows the centre as the785 bytes (114 words) - 11:29, 13 February 2009
- ...ll group elements which map the given subgroup to itself by [[Conjugation (group theory)|conjugation]].511 bytes (84 words) - 12:24, 29 December 2008
- In [[mathematics]], in the field of [[group theory]], the '''Baer-Specker group''', or '''Specker group''' is an example of an * {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago1 KB (151 words) - 16:18, 4 January 2013
- In [[group theory]], '''conjugacy''' is the relation between elements of a group that states ...d by [[Max Dehn]] in 1911 as one of three fundamental decision problems in group theory; the other two being the [[group isomorphism problem]] and the [[word probl802 bytes (124 words) - 01:13, 18 February 2009
- {{r|Character (group theory)}} {{r|Group theory}}762 bytes (99 words) - 17:00, 11 January 2010
- {{r|Order (group theory)}}248 bytes (33 words) - 17:37, 14 April 2010
- #REDIRECT [[Commutator#Group theory]]37 bytes (4 words) - 12:27, 8 November 2008
- #REDIRECT [[Order (group theory)]]34 bytes (4 words) - 17:56, 21 November 2008
- #REDIRECT [[Series (group theory)]]35 bytes (4 words) - 13:05, 8 November 2008
- #REDIRECT [[Order (group theory)]]34 bytes (4 words) - 07:44, 15 November 2008
- #REDIRECT [[Series (group theory)]]35 bytes (4 words) - 13:06, 8 November 2008
- #REDIRECT [[Series (group theory)]]35 bytes (4 words) - 13:07, 8 November 2008
- #REDIRECT [[Series (group theory)]]35 bytes (4 words) - 13:12, 8 November 2008
- #REDIRECT [[Commutator#Group theory]]37 bytes (4 words) - 12:25, 8 November 2008
- In the [[mathematics|mathematical]] field of [[group theory]], a group is '''residually ''X''''' (where ''X'' is some property of group959 bytes (139 words) - 15:07, 28 October 2008
- In group theory, this describes the relation between elements of a group that states that o168 bytes (26 words) - 01:13, 18 February 2009
- ==Group theory== In a [[group theory|group]], written multiplicatively, the commutator of elements ''x'' and ''y1 KB (217 words) - 15:16, 11 December 2008
- #REDIRECT [[Bona fide group theory]]36 bytes (5 words) - 19:33, 1 March 2008
- #REDIRECT [[Conjugation (group theory)#Inner automorphism]]59 bytes (6 words) - 14:26, 15 November 2008
- {{r|Group theory}}294 bytes (36 words) - 06:17, 15 June 2009
- In [[group theory]], a '''character''' may refer one of two related concepts: a [[group homom680 bytes (98 words) - 06:19, 15 June 2009
- * {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago802 bytes (112 words) - 03:33, 2 February 2009
- In mathematics, a component of group theory.80 bytes (10 words) - 10:38, 26 July 2023
- In mathematics, a component of group theory.80 bytes (10 words) - 10:38, 26 July 2023
- In mathematics, a component of group theory.80 bytes (10 words) - 10:40, 26 July 2023
- {{r|Center (group theory)}} {{r|Group theory}}656 bytes (94 words) - 12:34, 8 November 2008
- A concept in group theory on recovered element properties.95 bytes (12 words) - 19:00, 4 September 2009
- {{r|Conjugation (group theory)}} {{r|Group theory}}1 KB (187 words) - 20:18, 11 January 2010
- {{rpl|Conjugation (group theory)|In group theory|**}}278 bytes (33 words) - 05:59, 26 September 2013
- ...[group theory]], the set of [[permutation]]s on a set of objects form a [[group theory|group]], is called a '''permutation group''', with composition as the group2 KB (244 words) - 20:34, 1 July 2009
- In [[group theory]], a '''series''' is a [[chain (mathematics)]] of [[subgroup]]s of a [[grou1 KB (198 words) - 17:19, 6 December 2008
- In [[group theory]], the '''centraliser''' of a [[subset]] of a [[group (mathematics)]] is th676 bytes (115 words) - 12:19, 29 December 2008
- In [[group theory]], the '''Frattini subgroup''' is the intersection of all maximal [[subgrou583 bytes (84 words) - 05:33, 22 January 2009
- In [[group theory]], the '''order''' of a [[group (mathematics)|group]] element is the least857 bytes (146 words) - 13:24, 1 February 2009
- The automorphisms typically form a [[group theory|group]], the '''automorphism group''' of the structure.368 bytes (48 words) - 07:49, 5 February 2009
- In mathematics, a series in group theory that can be constructed by any data measured over time at regular intervals153 bytes (23 words) - 10:45, 26 July 2023
- ...d by [[Max Dehn]] in 1911 as one of three fundamental decision problems in group theory; the other two being the [[Word problem for groups|word problem]] and the [ ...us | coauthors = Abraham Karrass, Donald Solitar | title = Combinatorial group theory. Presentations of groups in terms of generators and relations | publisher1 KB (164 words) - 17:17, 28 October 2008
- In [[group theory]], a '''Sylow subgroup''' of a [[group (mathematics)|group]] is a [[subgrou * {{cite book | author=M. Aschbacher | title=Finite Group Theory | series=Cambridge studies in advanced mathematics | volume=10 | edition=2n1 KB (176 words) - 13:55, 7 February 2009
- by László Babai in his paper ''Trading group theory for randomness''<ref>530 bytes (75 words) - 18:06, 24 April 2012
- {{r|Character (group theory)|Character}}321 bytes (41 words) - 05:50, 15 June 2009
- * {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago227 bytes (28 words) - 16:21, 4 January 2013
- {{r|Group theory}}461 bytes (59 words) - 19:27, 11 January 2010
- {{r|Group theory}}1 KB (174 words) - 20:03, 11 January 2010
- {{r|Group theory}}508 bytes (64 words) - 17:00, 11 January 2010
- In mathematics, a component of group theory in which the factors of a normal series are central, as against chief and c173 bytes (26 words) - 10:33, 26 July 2023
- {{r|Conjugation (group theory)}}858 bytes (112 words) - 15:35, 11 January 2010
- {{r|Series (group theory)}}, a chain of subgroups of a group. Special types include794 bytes (118 words) - 02:53, 7 November 2008
- {{r|Series (group theory)}}, a chain of subgroups of a group.771 bytes (119 words) - 02:56, 7 November 2008
- {{r|Group theory}} {{r|Order (group theory)}}2 KB (247 words) - 17:28, 11 January 2010
- ...m Magnus | coauthors=Abraham Karrass, Donald Solitar | title=Combinatorial Group Theory | edition=2nd revised edition | publisher=[[Dover Publications]] | date=197595 bytes (73 words) - 17:25, 13 November 2008
- We shall expound the concept in [[group theory]]: very similar remarks apply to [[module theory]]. Exactness can be used to unify several concepts in group theory. For example, the assertion that the sequence3 KB (471 words) - 17:22, 15 November 2008
- ...tion''' is a function on [[positive integer]]s which gives the [[exponent (group theory)|exponent]] of the [[multiplicative group]] modulo that integer.796 bytes (127 words) - 15:10, 2 December 2008
- {{r|Group theory}} {{r|Conjugation (group theory)}}919 bytes (145 words) - 12:30, 29 December 2008
- {{r|Order (group theory)}}520 bytes (68 words) - 19:43, 11 January 2010
- Key concepts are [[Field extension|field extensions]] and [[Group theory|groups]], which should be thoroughly understood before Galois theory can b4 KB (683 words) - 22:17, 7 February 2010
- In [[group theory]], a '''subgroup''' of a [[group (mathematics)|group]] is a subset which is :'''Lagrange's Theorem''': In a finite group the [[order (group theory)|order]] of a subgroup multiplied by its index equals the order of the grou4 KB (631 words) - 07:56, 15 November 2008
- In [[group theory]], a [[subgroup]] ''H'' of a [[group]] ''G'' is termed '''characteristic'''2 KB (358 words) - 02:37, 18 November 2008
- In [[group theory]] a '''group homomorphism''' is a map from one [[group (mathematics)|group]1 KB (210 words) - 01:00, 11 February 2009
- {{r|Group theory}}436 bytes (56 words) - 11:13, 11 January 2010
- {{r|Conjugation (group theory)}}749 bytes (92 words) - 16:43, 11 January 2010
- * [[Composition series]] in [[group theory]]274 bytes (28 words) - 12:52, 31 May 2009
- *[http://www.cut-the-knot.org/proofs/PegsAndGroups.shtml Peg Solitaire and Group Theory]465 bytes (58 words) - 19:31, 14 September 2013
- ...s ''[[normal extension|normal]]'' if the automorphism group is of [[order (group theory)|order]] equal to ''d''.3 KB (418 words) - 12:18, 20 December 2008
- {{r|Group theory}}515 bytes (67 words) - 16:26, 11 January 2010
- {{r|Series (group theory)}}, a chain of subgroups of a group.1,018 bytes (163 words) - 02:50, 7 November 2008
- {{r|Character (group theory)}}217 bytes (25 words) - 03:39, 8 August 2009
- {{r|Group theory}}2 KB (247 words) - 06:00, 7 November 2010
- Auto-populated based on [[Special:WhatLinksHere/Order (group theory)]]. Needs checking by a human.594 bytes (76 words) - 19:15, 11 January 2010
- In [[group theory]], a '''free group''' is a group in which there is a ''generating set'' suc2 KB (436 words) - 02:56, 15 November 2008
- {{r|Group theory}}1 KB (187 words) - 19:18, 11 January 2010
- ...group modulo ''n'' and hence the totient function of ''n'' is the [[order (group theory)|order]] of ('''Z'''/''n'')<sup>*</sup>. By [[Lagrange's theorem]], the mu1 KB (224 words) - 17:35, 21 November 2008
- ...nction]] on the [[positive integer]]s which is derived from a [[character (group theory)|character]] on the [[multiplicative group]] taken [[modular arithmetic|mod2 KB (335 words) - 06:03, 15 June 2009
- {{r|Conjugation (group theory)}}739 bytes (92 words) - 17:31, 11 January 2010
- {{r|Group theory}}2 KB (262 words) - 19:07, 11 January 2010
- {{r|Series (group theory)}}, a chain of subgroups of a group.753 bytes (115 words) - 02:55, 7 November 2008
- In [[group theory]], '''conjugation''' is an operation between group elements. The '''conjug2 KB (294 words) - 04:53, 19 November 2008
- ...m Magnus | coauthors=Abraham Karrass, Donald Solitar | title=Combinatorial Group Theory | edition=2nd revised edition | publisher=[[Dover Publications]] | date=1971 KB (137 words) - 02:15, 29 November 2008
- In [[group theory]], a branch of [[mathematics]], the '''Vierergruppe''' (German, meaning gro3 KB (395 words) - 11:25, 30 July 2009
- {{r|Group theory}}910 bytes (146 words) - 16:55, 13 November 2008
- {{r|Group theory}}907 bytes (145 words) - 12:28, 29 December 2008
- {{r|Group theory}}449 bytes (57 words) - 19:59, 11 January 2010
- {{r|Group theory}}432 bytes (56 words) - 20:44, 11 January 2010
- {{r|Group theory}}997 bytes (156 words) - 14:41, 14 November 2008
- {{r|Conjugation (group theory)}}525 bytes (65 words) - 11:10, 11 January 2010
- Some common physical objects provide excellent introductions to [[group theory]].5 KB (819 words) - 10:52, 15 September 2009
- * A group acts on itself by [[Conjugation (group theory)conjugation]].4 KB (727 words) - 12:37, 16 November 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 way of s2 KB (338 words) - 16:43, 6 February 2009
- {{r|Character (group theory)}}645 bytes (81 words) - 21:03, 11 January 2010
- {{r|Series (group theory)}}634 bytes (95 words) - 13:59, 7 November 2008
- {{r|Series (group theory)}}636 bytes (95 words) - 13:59, 7 November 2008
- {{r|Series (group theory)}}630 bytes (95 words) - 14:00, 7 November 2008
- {{r|Series (group theory)}}635 bytes (95 words) - 14:00, 7 November 2008
- In [[group theory]], a branch of [[mathematics]], a '''normal [[subgroup]]''', also known as5 KB (785 words) - 09:22, 30 July 2009
- ...erlag |location= Braunschweig }} Translated into English: J. J. Griffin, ''Group Theory and its Application to the Quantum Mechanics of Atomic Spectra'', Academic2 KB (205 words) - 07:04, 30 July 2008
- ...le function]]s from a set to itself. It is a central object of study in [[group theory]]. The [[order (group theory)|order]] of <math>S_{n}</math> is given by the [[factorial]] function <math8 KB (1,392 words) - 20:52, 25 June 2009
- # Cyclic orders occur naturally in number theory ([[residue set]]s and group theory ([[cyclic group]]s, [[permutation]]s).2 KB (361 words) - 21:13, 6 January 2011
- ...generated by the elements of ''A'' together with all their [[conjugation (group theory)|conjugates]].2 KB (414 words) - 03:00, 14 February 2010
- {{r|Group theory}}846 bytes (136 words) - 06:40, 15 November 2008
- {{r|Group theory}}864 bytes (138 words) - 07:50, 30 July 2009
- {{r|Group theory}}885 bytes (141 words) - 12:30, 29 December 2008
- == History of group theory == ...are not solvable. This is one of the first important results to arise from group theory. The fact that <math>S_5</math> is not solvable gives a proof that there is15 KB (2,535 words) - 20:29, 14 February 2010
- *Mordeson J., Kiran R. Bhutani and Azriel Rosenfeld. ''Fuzzy Group Theory'', Springer Series: Studies in Fuzziness and Soft Computing, Vol. 182, 20054 KB (725 words) - 01:25, 12 December 2008
- ===Fraternal Interest Group Theory===11 KB (1,749 words) - 09:04, 8 June 2009
- ...mplex variables, usually denoted as [[SU(2)]], formally described as the [[group theory|group of transformations]] of two-dimensional complex vectors leaving their For example, see {{cite book |title=Group Theory: An Intuitive Approach |author=R. Mirman |chapter=§X.5 The unitary, unimod7 KB (1,096 words) - 05:49, 17 October 2013
- ...he set of integers with ''addition'' as the binary operation is a group. [[Group theory]] is the branch of mathematics which studies groups. Group theory originated with the work of [[Évariste Galois]], in 1830, on the problem o19 KB (3,074 words) - 11:11, 13 February 2009
- === Group theory, algebra and geometry ===7 KB (1,246 words) - 05:37, 18 October 2013
- László Babai, ''Trading group theory for randomness''.5 KB (793 words) - 05:49, 8 April 2024
- As first shown by Bethe by means of group theoretical [[character (group theory)|character relations]], there are no linear combinations of the five ''ℓ Group theory shows that for [[bra]], [[ket]], and operator all adapted to the same grou15 KB (2,390 words) - 10:11, 5 February 2010
- The theory of groups is studied in [[group theory]]. A major result in this theory is the [[classification of finite simple g18 KB (2,669 words) - 08:38, 17 April 2024
- ...rn mathematics necessary for basic modern number theory: complex analysis, group theory, Galois theory -- accompanied by greater rigor in analysis and abstraction in the sense of group theory. ("Solvable", in the sense of group theory, is27 KB (4,383 words) - 08:05, 11 October 2011
- ...ath>\mathcal{E}_\mathrm{X}</math> and <math>\mathcal{E}_\mathrm{Y}</math>. Group theory tells us that these energies are different, but without explicit calculatio Group theory tells us that a perturbation matrix element21 KB (3,426 words) - 23:58, 27 October 2013
- 9 KB (1,454 words) - 08:23, 18 October 2013
- In this way one can predict without knowledge of symmetry or group theory that certain dipoles vanish. For instance, the linear molecule O–C–O ha17 KB (2,690 words) - 01:15, 22 September 2009
- For a mathematical discussion see {{cite book |title=Group Theory: An Intuitive Approach |author=R. Mirman |chapter=§X.7 Angular momentum op20 KB (3,045 words) - 11:21, 29 June 2011
- ...procedure is elegant and not very tedious, but requires some knowledge of group theory, in particular knowledge of the connection between the irreducible represen22 KB (3,334 words) - 05:36, 6 March 2024
- ...weg Verlag, Braunschweig (1931). Translated into English: J. J. Griffin, ''Group Theory and its Application to the Quantum Mechanics of Atomic Spectra'' Academic P16 KB (2,632 words) - 04:33, 23 September 2021
- ...weg Verlag, Braunschweig (1931). Translated into English: J. J. Griffin, ''Group Theory and its Application to the Quantum Mechanics of Atomic Spectra'', Academic11 KB (1,671 words) - 06:37, 1 November 2009
- ...<ref name=LieAlgebra>For a mathematical discussion see {{cite book |title=Group Theory: An Intuitive Approach |author=R. Mirman |chapter=§X.7 Angular momentum op ...weg Verlag, Braunschweig (1931). Translated into English: J. J. Griffin, ''Group Theory and its Application to the Quantum Mechanics of Atomic Spectra'', Academic34 KB (5,282 words) - 14:21, 1 January 2011
- | [[Number theory]] || [[Set theory]] || [[Abstract algebra]] || [[Group theory]] || [[Order theory]]30 KB (4,289 words) - 16:03, 20 January 2023
- This result has an interesting [[group theory|group theoretical]] interpretation.<ref>The homogeneous polynomials of orde15 KB (2,490 words) - 12:23, 19 April 2009
- #[[Small Group Theory]]15 KB (2,070 words) - 08:57, 22 April 2024
- ...Statistical physics]], [[Statistical thermodynamics]], [[Graph theory]], [[Group Theory]], [[Monte Carlo simulations]], [[Scaling theory]], [[Physics of polymer so36 KB (5,455 words) - 11:49, 6 September 2013
- ...Statistical physics]], [[Statistical thermodynamics]], [[Graph theory]], [[Group Theory]], [[Monte Carlo simulations]], [[Scaling theory]], [[Physics of polymer so36 KB (5,455 words) - 08:57, 12 September 2013
- ...Weyl]] he wrote about chemical bonding theory from the point of view of [[group theory]].<ref>G. Rumer, E. Teller, and H. Weyl, ''Eine für die Valenztheorie geei28 KB (4,424 words) - 07:32, 20 April 2024
- ...]s<ref>László Babai. [http://portal.acm.org/citation.cfm?id=22192 "Trading group theory for randomness"]. ''Proceedings of the Seventeenth Annual Symposium on the32 KB (4,913 words) - 14:38, 18 March 2024
- ...]s<ref>László Babai. [http://portal.acm.org/citation.cfm?id=22192 "Trading group theory for randomness"]. ''Proceedings of the Seventeenth Annual Symposium on the32 KB (4,916 words) - 05:49, 8 April 2024
- The quantity in brackets is known in [[group theory]] as a [[Lie derivative]] of the full [[rotation group]] SO(3). In [[quantu23 KB (3,890 words) - 10:45, 11 June 2009
- ...m theory included [[Norbert Wiener]]'s work in controlling antiaircraft. [[Group theory]] and other mathematical esoterica were at the heart of the most critical [17 KB (2,638 words) - 09:26, 5 April 2024
- ...dynamics, and in mathematics turning to topics unrelated to calculus, like group theory. The leading German Romantic, [[Wolfgang von Goethe]], even tried to challe17 KB (2,625 words) - 19:47, 19 March 2023
- ...ery of the symmetries of roots of equations and thence to the invention of group theory, which finds routine application in the study of crystallographic groups by46 KB (6,635 words) - 13:25, 14 April 2021
- ...ng what the CZ policy on the matter has been discussed. For example, at [[group theory]], I originally typed up ''x'' * (''y'' * ''z'') and th44 KB (7,312 words) - 03:09, 8 March 2024