Maximal subgroup of finite nilpotent group - Revision history

Vipul at 15:10, 5 August 2009

2009-08-05T15:10:28Z

← Older revision		Revision as of 15:10, 5 August 2009
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	{{subgroup property}}		{{in-group subgroup property\|maximal subgroup\|finite nilpotent group}}

	==Definition==		==Definition==
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	===Stronger properties===		===Stronger properties===

	* [[Weaker than::Characteristic maximal subgroup in finite nilpotent group]]		* [[Weaker than::Characteristic maximal subgroup of finite nilpotent group]]
			* [[Weaker than::Maximal subgroup of group of prime power order]]
	===Weaker properties===		===Weaker properties===

	* [[Stronger than::Maximal subgroup in nilpotent group]]		* [[Stronger than::Maximal subgroup of nilpotent group]]
	* [[Stronger than::Maximal normal subgroup]]		* [[Stronger than::Maximal normal subgroup]]
	* [[Stronger than::Normal subgroup of prime index]]		* [[Stronger than::Normal subgroup of prime index]]
	* [[Stronger than::Maximal subgroup]]		* [[Stronger than::Maximal subgroup]]
	* [[Stronger than::Normal subgroup]]		* [[Stronger than::Normal subgroup]]
			* [[Stronger than::Order-normal subgroup]]
	* [[Stronger than::Isomorph-normal subgroup]]		* [[Stronger than::Isomorph-normal subgroup]]

Vipul: moved Maximal subgroup in finite nilpotent group to Maximal subgroup of finite nilpotent group

2009-08-05T15:09:29Z

moved Maximal subgroup in finite nilpotent group to Maximal subgroup of finite nilpotent group

← Older revision	Revision as of 15:09, 5 August 2009
(No difference)

Vipul: New page: {{subgroup property}} ==Definition== A '''maximal subgroup in finite nilpotent group''' is the following equivalent things: * A defining ingredient::maximal subgroup of a [[defining...

2009-03-04T23:18:21Z

New page: {{subgroup property}} ==Definition== A '''maximal subgroup in finite nilpotent group''' is the following equivalent things: * A defining ingredient::maximal subgroup of a [[defining...

New page

{{subgroup property}}

==Definition==

A '''maximal subgroup in finite nilpotent group''' is the following equivalent things:

* A [[defining ingredient::maximal subgroup]] of a [[defining ingredient::finite nilpotent group]].
* A [[defining ingredient::maximal normal subgroup]] of a [[defining ingredient::finite nilpotent group]].
* A [[defining ingredient::subgroup of prime index]] of a [[finite nilpotent group]].

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Characteristic maximal subgroup in finite nilpotent group]]

===Weaker properties===

* [[Stronger than::Maximal subgroup in nilpotent group]]
* [[Stronger than::Maximal normal subgroup]]
* [[Stronger than::Normal subgroup of prime index]]
* [[Stronger than::Maximal subgroup]]
* [[Stronger than::Normal subgroup]]
* [[Stronger than::Isomorph-normal subgroup]]