Monolithic group - Revision history

Vipul at 03:34, 17 December 2011

2011-12-17T03:34:45Z

← Older revision		Revision as of 03:34, 17 December 2011
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			[[Importance rank::3\| ]]
	{{group property}}		{{group property}}

	{{variationof\|simplicity}}		{{variationof\|simplicity}}

Vipul at 16:38, 30 August 2008

2008-08-30T16:38:19Z

← Older revision		Revision as of 16:38, 30 August 2008
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	===Symbol-free definition===		===Symbol-free definition===

	A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]], and this is contained in ''every'' nontrivial [[defining ingredient::normal subgroup]]). This minimal normal subgroup is termed a '''monolith'''.		A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]], and this is contained in ''every'' nontrivial [[defining ingredient::normal subgroup]]. This minimal normal subgroup is termed a '''monolith'''.

	==Relation with other properties==		==Relation with other properties==

Vipul at 18:16, 21 August 2008

2008-08-21T18:16:39Z

← Older revision		Revision as of 18:16, 21 August 2008
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	===Symbol-free definition===		===Symbol-free definition===

	A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]] ~~(in other words~~, ~~there~~ is ~~a [[nontrivial normal subgroup]]~~ contained in ''every'' nontrivial [[defining ingredient::normal subgroup]]). This minimal normal subgroup is termed a '''monolith'''.		A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]], and this is contained in ''every'' nontrivial [[defining ingredient::normal subgroup]]). This minimal normal subgroup is termed a '''monolith'''.

	==Relation with other properties==		==Relation with other properties==
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	===Stronger properties===		===Stronger properties===

	* [[~~weaker~~ than::Simple group]]		* [[Weaker than::Simple group]]

			===Weaker properties===

			* [[Stronger than::Subdirectly irreducible group]]
			* [[Stronger than::Directly indecomposable group]]

	===Related properties===		===Related properties===

	* [[One-headed group]]		* [[One-headed group]]

Vipul: /* Relation with other properties */

2008-06-20T11:10:31Z

Relation with other properties

← Older revision		Revision as of 11:10, 20 June 2008
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	* [[weaker than::Simple group]]		* [[weaker than::Simple group]]
	* [[weaker than::Jordan-unique group]]

	===Related properties===		===Related properties===

	* [[One-headed group]]		* [[One-headed group]]

Vipul at 11:10, 20 June 2008

2008-06-20T11:10:04Z

← Older revision		Revision as of 11:10, 20 June 2008
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	===Symbol-free definition===		===Symbol-free definition===

	A [[group]] is said to be '''monolithic''' if it has a unique [[minimal normal subgroup]]. This minimal normal subgroup is termed a '''monolith'''.		A [[group]] is said to be '''monolithic''' if it has a unique [[defining ingredient::minimal normal subgroup]] (in other words, there is a [[nontrivial normal subgroup]] contained in ''every'' nontrivial [[defining ingredient::normal subgroup]]). This minimal normal subgroup is termed a '''monolith'''.

	==Relation with other properties==		==Relation with other properties==
Line 13:		Line 13:
	===Stronger properties===		===Stronger properties===

	* [[Simple group]]		* [[weaker than::Simple group]]
	* [[Jordan-unique group]]		* [[weaker than::Jordan-unique group]]

	===Related properties===		===Related properties===

	* [[One-headed group]]		* [[One-headed group]]

Vipul: 1 revision

2008-05-07T23:51:23Z

1 revision

← Older revision	Revision as of 23:51, 7 May 2008
(No difference)

Vipul at 16:22, 6 March 2007

2007-03-06T16:22:21Z

New page

{{group property}}

{{variationof|simplicity}}

==Definition==

===Symbol-free definition===

A [[group]] is said to be '''monolithic''' if it has a unique [[minimal normal subgroup]]. This minimal normal subgroup is termed a '''monolith'''.

==Relation with other properties==

===Stronger properties===

* [[Simple group]]
* [[Jordan-unique group]]

===Related properties===

* [[One-headed group]]