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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
  • ...'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>&minus;1</sup>'' &isin; ''H'', then ''H'' is a normal subgroup of ''G'', (also expressed as "''H'' is invariant in ''G''"). That is, with
    5 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-tri
    802 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
  • 117 bytes (19 words) - 14:39, 14 November 2008
  • 138 bytes (18 words) - 14:57, 14 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
  • {{r|Characteristic subgroup}} {{r|Essential subgroup}}
    997 bytes (156 words) - 14:41, 14 November 2008
  • Subgroup N of a group G where every expression g-1ng is in N for every g in G and ev
    132 bytes (27 words) - 10:17, 4 September 2009

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 define
    511 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|ta
    518 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-tri
    802 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|Aviation}}
    21 bytes (2 words) - 12:10, 21 January 2014
  • {{Subgroup|Virology}}
    21 bytes (2 words) - 05:08, 14 May 2023
  • {{Aquatics Subgroup}}
    21 bytes (2 words) - 07:34, 7 March 2010
  • {{Nephrology subgroup}}
    23 bytes (2 words) - 12:18, 11 March 2021
  • {{Europe Subgroup}}
    19 bytes (2 words) - 07:32, 24 October 2014
  • {{Ecology Subgroup}}
    20 bytes (2 words) - 16:54, 16 May 2023
  • {{Pseudoscience Subgroup}}
    26 bytes (2 words) - 17:25, 13 September 2020
  • {{Boxing Subgroup}}
    19 bytes (2 words) - 07:38, 7 March 2010
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