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- In [[group theory]], a '''subgroup''' of a [[group (mathematics)|group]] is a subset which is itself a group w Formally, a subset ''S'' of a group ''G'' is a subgroup if it satisfies the following conditions:4 KB (631 words) - 07:56, 15 November 2008
- 117 bytes (19 words) - 14:39, 14 November 2008
- 138 bytes (18 words) - 14:57, 14 November 2008
- ...'invariant subgroup''', or '''normal divisor''', is a (proper or improper) subgroup ''H'' of the [[group]] ''G'' that is invariant under [[conjugation]] by all ...that: ''g h g<sup>−1</sup>'' ∈ ''H'', then ''H'' is a normal subgroup of ''G'', (also expressed as "''H'' is invariant in ''G''"). That is, with5 KB (785 words) - 09:22, 30 July 2009
- In [[group theory]], a [[subgroup]] ''H'' of a [[group]] ''G'' is termed '''characteristic''' if it mapped to Any characteristic subgroup of a group is [[normal subgroup|normal]], but the converse does not always hold.2 KB (358 words) - 02:37, 18 November 2008
- ...tudying the theory of [[abelian group]]s, an '''essential subgroup''' is a subgroup that determines much of the structure of its containing group. ...>G</math> is said to be '''essential''' if whenever ''H'' is a non-trivial subgroup of ''G'', the intersection of ''S'' and ''H'' is non-trivial: here "non-tri802 bytes (112 words) - 03:33, 2 February 2009
- 37 bytes (4 words) - 12:25, 8 November 2008
- #REDIRECT [[Subgroup#Maximal subgroup]]39 bytes (4 words) - 17:54, 14 November 2008
- #REDIRECT [[Normal subgroup]]29 bytes (3 words) - 09:24, 30 July 2009
- ...theory]], the '''Frattini subgroup''' is the intersection of all maximal [[subgroup]]s of a group. where ''M'' runs over all [[maximal subgroup]]s of G. If ''G'' has no maximal subgroups then <math>\Phi(G) = G</math>.583 bytes (84 words) - 05:33, 22 January 2009
- ...alled a '''Sylow''' '''''p''''' '''-subgroup''' or a '''''p''''' '''-Sylow subgroup'''. ...e subgroup of ''G'' of order <math>p^s</math>, which is thus a Sylow ''p''-subgroup.1 KB (176 words) - 13:55, 7 February 2009
- A subgroup of a finite group whose order is the largest possible power of one of the p155 bytes (26 words) - 13:13, 5 December 2008
- ...of a group which has non-trivial intersection with every other non-trivial subgroup.131 bytes (17 words) - 02:12, 6 December 2008
- A subgroup which is mapped to itself by any automorphism of the whole group.112 bytes (17 words) - 16:19, 6 November 2008
- 89 bytes (12 words) - 15:05, 14 November 2008
- The subgroup of a group generated by all commutators.89 bytes (12 words) - 15:07, 14 November 2008
- 12 bytes (1 word) - 05:05, 26 September 2007
- 138 bytes (18 words) - 15:34, 14 November 2008
- 12 bytes (1 word) - 04:20, 11 November 2007
- 138 bytes (18 words) - 17:04, 6 November 2008
- #REDIRECT [[Characteristic subgroup]]37 bytes (3 words) - 02:38, 18 November 2008
- Subgroup N of a group G where every expression g-1ng is in N for every g in G and ev132 bytes (27 words) - 10:17, 4 September 2009
- {{r|Characteristic subgroup}} {{r|Essential subgroup}}997 bytes (156 words) - 14:41, 14 November 2008
- {{Anarchism Subgroup}} ...hought appropriated this term. May be someday one will create "libertarian subgroup"? It is obvious that "Libertarian parties", minarchists, conservatives have22 KB (3,552 words) - 14:27, 31 March 2024
- {{Castle Subgroup}}19 bytes (2 words) - 06:21, 22 November 2020
- {{Cardiovascular Subgroup}}410 bytes (59 words) - 19:04, 16 April 2009
- {{Boxing Subgroup}}19 bytes (2 words) - 07:38, 7 March 2010
- {{Africa Subgroup}}19 bytes (2 words) - 11:00, 21 December 2020
- {{Subgroup|Medicine}}21 bytes (2 words) - 16:58, 13 May 2023
- {{Cycling Subgroup}}20 bytes (2 words) - 07:50, 7 March 2010
- {{Dogs Subgroup}}5 KB (826 words) - 10:48, 11 March 2021
- {{Japan Subgroup}} == Handling overlap with Pacific War Subgroup ==910 bytes (138 words) - 02:29, 30 December 2010
- {{Asia Subgroup}}17 bytes (2 words) - 13:11, 21 December 2020
- {{Subgroup|Zoology}}20 bytes (2 words) - 16:07, 13 May 2023
- {{Subgroup|Immunology}}23 bytes (2 words) - 16:58, 13 May 2023
- {{Transportation Subgroup}}27 bytes (2 words) - 06:47, 14 November 2013
- {{Security Subgroup}} I've never set up a subgroup, and it doesn't yet seem to be working. So far, I ''think'' I've added myse3 KB (428 words) - 14:37, 18 March 2024
- {{subgroup|Orthopedics|Health Sciences}}40 bytes (4 words) - 09:30, 5 August 2010
- 0 bytes (0 words) - 08:31, 5 February 2024
- {{Athletics Subgroup}}22 bytes (2 words) - 18:38, 5 March 2010
- {{China Subgroup}}18 bytes (2 words) - 01:45, 30 December 2010
- {{Botany Subgroup}} #Make a nice home page for the subgroup3 KB (471 words) - 11:04, 8 March 2009
- {{Subgroup|Physiology}}23 bytes (2 words) - 16:59, 13 May 2023
- {{Skiing Subgroup}}19 bytes (2 words) - 07:54, 7 March 2010
- {{Scotland Subgroup}}21 bytes (2 words) - 17:46, 3 December 2013
- {{r|Normal subgroup}} {{r|Frattini subgroup}}656 bytes (94 words) - 12:34, 8 November 2008
- {{subgroup|Toxicology|Health Sciences|Chemistry}}49 bytes (5 words) - 15:16, 5 August 2010
- {{Horror Subgroup}}162 bytes (18 words) - 01:09, 9 January 2011
- {{Bowling Subgroup}}20 bytes (2 words) - 12:44, 25 February 2021
- {{Phonology Subgroup}}22 bytes (2 words) - 23:17, 15 March 2009
- {{Pharmacology Subgroup}}408 bytes (59 words) - 19:03, 16 April 2009
- {{Paranormal Subgroup}}145 bytes (18 words) - 12:51, 16 January 2014
- {{subgroup|Intelligence|Military|Politics|Economics}}53 bytes (5 words) - 13:47, 8 August 2010
- {{Subgroup|Neuroendocrinology}}31 bytes (2 words) - 17:43, 13 May 2023
- {{r|Subgroup}} {{r|Characteristic subgroup}}872 bytes (138 words) - 15:32, 14 November 2008
- {{Tennis Subgroup}}19 bytes (2 words) - 10:46, 6 March 2010
- {{Hematology subgroup}}23 bytes (2 words) - 12:17, 11 March 2021
- Auto-populated based on [[Special:WhatLinksHere/Frattini subgroup]]. Needs checking by a human. {{r|Characteristic subgroup}}483 bytes (61 words) - 16:40, 11 January 2010
- {{subgroup|Aviation}}21 bytes (2 words) - 12:10, 21 January 2014
- {{Genetics Subgroup}}21 bytes (2 words) - 13:24, 27 February 2010
- {{Subgroup|Neuroscience}}25 bytes (2 words) - 04:35, 14 May 2023
- {{Microbiology Subgroup}}759 bytes (117 words) - 02:22, 4 April 2009
- {{Golf Subgroup}}17 bytes (2 words) - 11:54, 6 March 2010
- {{Nephrology subgroup}}23 bytes (2 words) - 12:18, 11 March 2021
- {{Ecology Subgroup}}20 bytes (2 words) - 16:54, 16 May 2023
- Auto-populated based on [[Special:WhatLinksHere/Sylow subgroup]]. Needs checking by a human.432 bytes (56 words) - 20:44, 11 January 2010
- {{Europe Subgroup}}19 bytes (2 words) - 07:32, 24 October 2014
- {{Subgroup|Virology}}21 bytes (2 words) - 05:08, 14 May 2023
- Auto-populated based on [[Special:WhatLinksHere/Essential subgroup]]. Needs checking by a human. {{r|Subgroup}}432 bytes (55 words) - 16:23, 11 January 2010
- {{Gastroenterology subgroup}}381 bytes (40 words) - 11:18, 10 June 2010
- {{Pseudoscience Subgroup}}26 bytes (2 words) - 17:25, 13 September 2020
- #REDIRECT [[Subgroup#Index]]28 bytes (3 words) - 02:54, 15 November 2008
- {{Biochemistry Subgroup}}413 bytes (66 words) - 12:09, 6 April 2009
- {{Baseball Subgroup}}21 bytes (2 words) - 07:05, 7 March 2010
- {{subgroup|radiology|Health Sciences|Physics|Engineering}}58 bytes (6 words) - 04:20, 10 February 2011
- {{Subgroup|American Literature}} There's already a Literature Workgroup. Why a subgroup as well? [[User:Peter Jackson|Peter Jackson]] ([[User talk:Peter Jackson|ta518 bytes (76 words) - 10:03, 10 May 2023
- {{cardiology subgroup}}1 KB (110 words) - 02:11, 11 June 2010
- {{France Subgroup}}467 bytes (69 words) - 10:19, 15 May 2017
- {{Philately Subgroup}}22 bytes (2 words) - 16:25, 17 November 2020
- {{Anatomy Subgroup}}20 bytes (2 words) - 01:51, 4 April 2009
- {{Basketball Subgroup}}23 bytes (2 words) - 07:08, 7 March 2010
- {{Korea Subgroup}}18 bytes (2 words) - 00:03, 13 November 2011
- #REDIRECT [[CZ Talk:American Literature Subgroup]]50 bytes (6 words) - 10:03, 10 May 2023
- {{Dance Subgroup}}3 KB (336 words) - 10:51, 11 March 2021
- {{Phonetics Subgroup}}22 bytes (2 words) - 03:35, 7 August 2009
- #REDIRECT [[CZ Talk:Association football Subgroup]]51 bytes (6 words) - 02:33, 24 September 2019
- {{India Subgroup}}18 bytes (2 words) - 06:20, 22 November 2020
- 0 bytes (0 words) - 00:28, 27 May 2023
- {{Aquatics Subgroup}}21 bytes (2 words) - 07:34, 7 March 2010
- {{Film Subgroup}}17 bytes (2 words) - 18:49, 28 August 2013
- {{Gaelic football Subgroup}}28 bytes (3 words) - 14:06, 4 March 2010
- {{Written Language Subgroup}}29 bytes (3 words) - 07:19, 18 September 2013
- {{Subgroup|British History}}28 bytes (3 words) - 16:06, 11 May 2023
- {{Subgroup|Image analysis}}27 bytes (3 words) - 04:54, 14 May 2023
- {{Science fiction Subgroup}}28 bytes (3 words) - 00:33, 19 January 2010
- {{Emergency management subgroup}}33 bytes (3 words) - 17:42, 17 July 2010
- {{Canadian football Subgroup}}30 bytes (3 words) - 14:28, 4 March 2010
- 0 bytes (0 words) - 08:08, 5 February 2024
- {{Olympic Games Subgroup}}26 bytes (3 words) - 17:51, 5 March 2010
- {{Ice hockey Subgroup}}23 bytes (3 words) - 07:52, 7 March 2010
Page text matches
- ...theory]], the '''Frattini subgroup''' is the intersection of all maximal [[subgroup]]s of a group. where ''M'' runs over all [[maximal subgroup]]s of G. If ''G'' has no maximal subgroups then <math>\Phi(G) = G</math>.583 bytes (84 words) - 05:33, 22 January 2009
- #REDIRECT [[Subgroup#Maximal subgroup]]39 bytes (4 words) - 17:54, 14 November 2008
- ...group (mathematics)]] is the set of all group elements which map the given subgroup to itself by [[Conjugation (group theory)|conjugation]]. Formally, for ''H'' a subgroup of a group ''G'', we define511 bytes (84 words) - 12:24, 29 December 2008
- {{Subgroup|American Literature}} There's already a Literature Workgroup. Why a subgroup as well? [[User:Peter Jackson|Peter Jackson]] ([[User talk:Peter Jackson|ta518 bytes (76 words) - 10:03, 10 May 2023
- In [[group theory]], a '''series''' is a [[chain (mathematics)]] of [[subgroup]]s of a [[group (mathematics)|group]] ordered by [[subset]] [[inclusion]]. ...</math>. A subinvariant series in which each subgroup is a maximal normal subgroup of its predecessor is a '''composition series'''.1 KB (198 words) - 17:19, 6 December 2008
- ...of a group which has non-trivial intersection with every other non-trivial subgroup.131 bytes (17 words) - 02:12, 6 December 2008
- ...alled a '''Sylow''' '''''p''''' '''-subgroup''' or a '''''p''''' '''-Sylow subgroup'''. ...e subgroup of ''G'' of order <math>p^s</math>, which is thus a Sylow ''p''-subgroup.1 KB (176 words) - 13:55, 7 February 2009
- Auto-populated based on [[Special:WhatLinksHere/Frattini subgroup]]. Needs checking by a human. {{r|Characteristic subgroup}}483 bytes (61 words) - 16:40, 11 January 2010
- In [[group theory]], a [[subgroup]] ''H'' of a [[group]] ''G'' is termed '''characteristic''' if it mapped to Any characteristic subgroup of a group is [[normal subgroup|normal]], but the converse does not always hold.2 KB (358 words) - 02:37, 18 November 2008
- ...tudying the theory of [[abelian group]]s, an '''essential subgroup''' is a subgroup that determines much of the structure of its containing group. ...>G</math> is said to be '''essential''' if whenever ''H'' is a non-trivial subgroup of ''G'', the intersection of ''S'' and ''H'' is non-trivial: here "non-tri802 bytes (112 words) - 03:33, 2 February 2009
- {{r|Characteristic subgroup}} {{r|Essential subgroup}}997 bytes (156 words) - 14:41, 14 November 2008
- {{Japan Subgroup}} == Handling overlap with Pacific War Subgroup ==910 bytes (138 words) - 02:29, 30 December 2010
- {{Subgroup|Medicine}}21 bytes (2 words) - 16:58, 13 May 2023
- {{Genetics Subgroup}}21 bytes (2 words) - 13:24, 27 February 2010
- {{Golf Subgroup}}17 bytes (2 words) - 11:54, 6 March 2010
- {{Bowling Subgroup}}20 bytes (2 words) - 12:44, 25 February 2021
- {{Scotland Subgroup}}21 bytes (2 words) - 17:46, 3 December 2013
- {{Subgroup|Immunology}}23 bytes (2 words) - 16:58, 13 May 2023
- {{Subgroup|Neuroendocrinology}}31 bytes (2 words) - 17:43, 13 May 2023
- {{Hematology subgroup}}23 bytes (2 words) - 12:17, 11 March 2021
- {{Subgroup|Physiology}}23 bytes (2 words) - 16:59, 13 May 2023
- {{Subgroup|Neuroscience}}25 bytes (2 words) - 04:35, 14 May 2023
- {{Baseball Subgroup}}21 bytes (2 words) - 07:05, 7 March 2010
- {{Nephrology subgroup}}23 bytes (2 words) - 12:18, 11 March 2021
- {{Phonology Subgroup}}22 bytes (2 words) - 23:17, 15 March 2009
- {{subgroup|Aviation}}21 bytes (2 words) - 12:10, 21 January 2014
- {{Subgroup|Zoology}}20 bytes (2 words) - 16:07, 13 May 2023
- {{Subgroup|Virology}}21 bytes (2 words) - 05:08, 14 May 2023
- {{Basketball Subgroup}}23 bytes (2 words) - 07:08, 7 March 2010
- {{Europe Subgroup}}19 bytes (2 words) - 07:32, 24 October 2014
- {{Pseudoscience Subgroup}}26 bytes (2 words) - 17:25, 13 September 2020
- {{Aquatics Subgroup}}21 bytes (2 words) - 07:34, 7 March 2010
- {{Korea Subgroup}}18 bytes (2 words) - 00:03, 13 November 2011
- {{Ecology Subgroup}}20 bytes (2 words) - 16:54, 16 May 2023
- {{Philately Subgroup}}22 bytes (2 words) - 16:25, 17 November 2020
- {{Boxing Subgroup}}19 bytes (2 words) - 07:38, 7 March 2010
- {{Film Subgroup}}17 bytes (2 words) - 18:49, 28 August 2013
- {{India Subgroup}}18 bytes (2 words) - 06:20, 22 November 2020
- {{Cycling Subgroup}}20 bytes (2 words) - 07:50, 7 March 2010
- {{Castle Subgroup}}19 bytes (2 words) - 06:21, 22 November 2020
- {{Athletics Subgroup}}22 bytes (2 words) - 18:38, 5 March 2010
- {{Africa Subgroup}}19 bytes (2 words) - 11:00, 21 December 2020
- {{Skiing Subgroup}}19 bytes (2 words) - 07:54, 7 March 2010
- {{Anatomy Subgroup}}20 bytes (2 words) - 01:51, 4 April 2009
- {{China Subgroup}}18 bytes (2 words) - 01:45, 30 December 2010
- {{Asia Subgroup}}17 bytes (2 words) - 13:11, 21 December 2020
- {{Phonetics Subgroup}}22 bytes (2 words) - 03:35, 7 August 2009
- {{Transportation Subgroup}}27 bytes (2 words) - 06:47, 14 November 2013
- {{Football Subgroup}}21 bytes (2 words) - 02:33, 24 September 2019
- {{Tennis Subgroup}}19 bytes (2 words) - 10:46, 6 March 2010
- #REDIRECT [[Sylow subgroup]]28 bytes (3 words) - 18:02, 6 December 2008
- {{Social Policy Subgroup}}26 bytes (3 words) - 14:06, 8 October 2019
- {{Motor racing Subgroup}}25 bytes (3 words) - 02:34, 7 March 2010
- #REDIRECT [[Characteristic subgroup]]37 bytes (3 words) - 02:38, 18 November 2008
- {{Subgroup|Differential geometry}}34 bytes (3 words) - 04:49, 14 May 2023
- #REDIRECT [[Subgroup#Cosets]]29 bytes (3 words) - 14:56, 14 November 2008
- {{Signals intelligence Subgroup}}33 bytes (3 words) - 06:47, 22 March 2021
- {{American football Subgroup}}30 bytes (3 words) - 00:46, 4 March 2010
- {{Subgroup|Image analysis}}27 bytes (3 words) - 04:54, 14 May 2023
- {{Language Acquisition Subgroup}}33 bytes (3 words) - 07:46, 24 March 2009
- {{Science fiction Subgroup}}28 bytes (3 words) - 00:33, 19 January 2010
- {{American History Subgroup}}29 bytes (3 words) - 16:24, 14 May 2023
- {{Gaelic football Subgroup}}28 bytes (3 words) - 14:06, 4 March 2010
- {{Environmental Science Subgroup}}34 bytes (3 words) - 16:57, 16 May 2023
- {{Canadian football Subgroup}}30 bytes (3 words) - 14:28, 4 March 2010
- #REDIRECT [[Normal subgroup]]29 bytes (3 words) - 09:24, 30 July 2009
- {{Written Language Subgroup}}29 bytes (3 words) - 07:19, 18 September 2013
- {{Subgroup|English Literature}}31 bytes (3 words) - 15:57, 11 May 2023
- {{Infectious Disease Subgroup}}31 bytes (3 words) - 01:10, 4 April 2009
- {{Emergency management subgroup}}33 bytes (3 words) - 17:42, 17 July 2010
- {{Olympic Games Subgroup}}26 bytes (3 words) - 17:51, 5 March 2010
- #REDIRECT [[Normal subgroup]]29 bytes (3 words) - 09:24, 30 July 2009
- {{Ice hockey Subgroup}}23 bytes (3 words) - 07:52, 7 March 2010
- {{Subgroup|British History}}28 bytes (3 words) - 16:06, 11 May 2023
- #REDIRECT [[Subgroup#Index]]28 bytes (3 words) - 02:54, 15 November 2008
- {{Martial Arts Subgroup}}25 bytes (3 words) - 02:34, 24 September 2019
- #REDIRECT [[Subgroup#Index]]28 bytes (3 words) - 02:54, 15 November 2008
- {{African American Subgroup}}29 bytes (3 words) - 10:31, 27 December 2020
- {{Australian rules football Subgroup}}38 bytes (4 words) - 14:00, 2 March 2010
- {{Rugby union football Subgroup}}33 bytes (4 words) - 02:39, 24 September 2019
- {{Rugby league football Subgroup}}34 bytes (4 words) - 02:36, 24 September 2019
- {{History of Technology Subgroup}}34 bytes (4 words) - 10:45, 27 February 2010
- {{subgroup|Orthopedics|Health Sciences}}40 bytes (4 words) - 09:30, 5 August 2010
- {{r|Normal subgroup}} {{r|Frattini subgroup}}656 bytes (94 words) - 12:34, 8 November 2008
- {{subgroup|Intelligence|Military|Politics|Economics}}53 bytes (5 words) - 13:47, 8 August 2010
- {{subgroup|United States Army|Military}}40 bytes (5 words) - 03:07, 9 August 2010
- {{subgroup|Complementary and alternative medicine}}51 bytes (5 words) - 13:07, 6 September 2013
- {{subgroup|Commercial aviation|Engineering|Economics}}54 bytes (5 words) - 10:46, 13 February 2011
- {{Subgroup|Weapons of mass destruction}}40 bytes (5 words) - 00:09, 27 May 2023
- {{Spanish Missions in California Subgroup}}43 bytes (5 words) - 09:43, 2 October 2013
- #REDIRECT [[Normal subgroup#Quotient group]]44 bytes (5 words) - 11:49, 31 December 2008
- {{subgroup|Toxicology|Health Sciences|Chemistry}}49 bytes (5 words) - 15:16, 5 August 2010
- #REDIRECT [[CZ Talk:Social policy Subgroup]]44 bytes (6 words) - 14:06, 8 October 2019
- {{subgroup|Medical informatics|Health Sciences|Computers}}58 bytes (6 words) - 17:44, 9 February 2011
- {{subgroup|United States Navy|Military|History}}48 bytes (6 words) - 13:31, 12 August 2010
- {{subgroup|radiology|Health Sciences|Physics|Engineering}}58 bytes (6 words) - 04:20, 10 February 2011
- {{subgroup|Pacific War|Military|History|Politics}}50 bytes (6 words) - 16:31, 6 September 2010
- #REDIRECT [[CZ Talk:American Literature Subgroup]]50 bytes (6 words) - 10:03, 10 May 2023
- #REDIRECT [[CZ Talk:Association football Subgroup]]51 bytes (6 words) - 02:33, 24 September 2019
- #REDIRECT [[CZ Talk:Martial arts Subgroup]]43 bytes (6 words) - 02:34, 24 September 2019