Normal subgroup - Revision history

Vipul at 12:30, 29 December 2009

2009-12-29T12:30:56Z

← Older revision		Revision as of 12:30, 29 December 2009
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	Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].		Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].

	Primary subject wiki entry: [[Groupprops:Normal subgroup]].		Primary subject wiki entry: [[Groupprops:Normal subgroup]]. See also [[Groupprops:Questions:Normal subgroup]].

	Other subject wiki entries: [[Diffgeom:Normal subgroup]]		Other subject wiki entries: [[Diffgeom:Normal subgroup]]

Vipul at 01:16, 21 March 2009

2009-03-21T01:16:35Z

← Older revision		Revision as of 01:16, 21 March 2009
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	'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.		'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.

	Related terms: Normality (the property of a subgroup being normal), [[Groupprops:Normal core\|normal core]] (the largest normal subgroup contained in a given subgroup), [[Groupprops:Normal closure\|normal closure]] (the smallest normal subgroup containing a given subgroup), [[Groupprops:Normalizer\|normalizer]] (the largest subgroup containing a given subgroup, in which it is normal), [[Groupprops:Normal automorphism\|normal automorphism]] (an automorphism that ~~preserves~~ every normal subgroup)		Related terms: Normality (the property of a subgroup being normal), [[Groupprops:Normal core\|normal core]] (the largest normal subgroup contained in a given subgroup), [[Groupprops:Normal closure\|normal closure]] (the smallest normal subgroup containing a given subgroup), [[Groupprops:Normalizer\|normalizer]] (the largest subgroup containing a given subgroup, in which it is normal), [[Groupprops:Normal automorphism\|normal automorphism]] (an automorphism that restricts to an automorphism on every normal subgroup).

	Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].		Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].

Vipul at 01:16, 21 March 2009

2009-03-21T01:16:03Z

← Older revision		Revision as of 01:16, 21 March 2009
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	Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].		Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].

	Primary subject wiki entry: [[Groupprops:Normal subgroup]]		Primary subject wiki entry: [[Groupprops:Normal subgroup]].

	Other subject wiki entries: [[Diffgeom:Normal subgroup]]		Other subject wiki entries: [[Diffgeom:Normal subgroup]]

			Coverage in guided tours: Groupprops guided tour for beginners; section not yet prepared.

	Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690\|Springer Online Reference Works]], [[Citizendium:Normal subgroup]]		Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690\|Springer Online Reference Works]], [[Citizendium:Normal subgroup]]

Vipul at 18:16, 22 May 2008

2008-05-22T18:16:35Z

← Older revision		Revision as of 18:16, 22 May 2008
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	'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.		'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.

	Related terms: Normality (the property of a subgroup being normal), [[Groupprops:Normal core\|normal core]] (the largest normal subgroup contained in a given subgroup), [[Groupprops:Normal closure\|normal closure]] (the smallest normal subgroup containing a given subgroup), [[Groupprops:Normalizer\|normalizer]] (the largest subgroup containing a given subgroup, in which it is normal).		Related terms: Normality (the property of a subgroup being normal), [[Groupprops:Normal core\|normal core]] (the largest normal subgroup contained in a given subgroup), [[Groupprops:Normal closure\|normal closure]] (the smallest normal subgroup containing a given subgroup), [[Groupprops:Normalizer\|normalizer]] (the largest subgroup containing a given subgroup, in which it is normal), [[Groupprops:Normal automorphism\|normal automorphism]] (an automorphism that preserves every normal subgroup)

	Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].		Term variations: [[Groupprops:Subnormal subgroup\|subnormal subgroup]], [[Groupprops:Abnormal subgroup\|abnormal subgroup]], [[Groupprops:Quasinormal subgroup\|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].

Vipul at 13:32, 16 May 2008

2008-05-16T13:32:47Z

← Older revision		Revision as of 13:32, 16 May 2008
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	Other subject wiki entries: [[Diffgeom:Normal subgroup]]		Other subject wiki entries: [[Diffgeom:Normal subgroup]]

	Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690]], [[Citizendium:Normal subgroup]]		Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690\|Springer Online Reference Works]], [[Citizendium:Normal subgroup]]

Vipul at 16:23, 14 May 2008

2008-05-14T16:23:53Z

← Older revision		Revision as of 16:23, 14 May 2008
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	<noinclude>[[Status::Basic definition\|~~:Basic definition~~]][[Topic::Group theory]][[Primary wiki::Groupprops]]</noinclude>		<noinclude>[[Status::Basic definition\| ]][[Topic::Group theory\| ]][[Primary wiki::Groupprops\| ]]</noinclude>
	'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.		'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.

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	Other subject wiki entries: [[Diffgeom:Normal subgroup]]		Other subject wiki entries: [[Diffgeom:Normal subgroup]]

	Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690]], [[Citizendium::Normal subgroup]]		Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690]], [[Citizendium:Normal subgroup]]

Vipul: New page: Status::Basic definition|Topic::Group theoryPrimary wiki::Groupprops '''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorp...

2008-05-14T16:20:14Z

New page: <noinclude>Status::Basic definition Topic::Group theory Primary wiki::Groupprops</noinclude> '''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorp...

New page

<noinclude>[[Status::Basic definition|:Basic definition]][[Topic::Group theory]][[Primary wiki::Groupprops]]</noinclude>
'''Normal subgroup''': A subgroup of a group that occurs as the kernel of a homomorphism, or equivalently, such that every left coset and right coset are equal.

Related terms: Normality (the property of a subgroup being normal), [[Groupprops:Normal core|normal core]] (the largest normal subgroup contained in a given subgroup), [[Groupprops:Normal closure|normal closure]] (the smallest normal subgroup containing a given subgroup), [[Groupprops:Normalizer|normalizer]] (the largest subgroup containing a given subgroup, in which it is normal).

Term variations: [[Groupprops:Subnormal subgroup|subnormal subgroup]], [[Groupprops:Abnormal subgroup|abnormal subgroup]], [[Groupprops:Quasinormal subgroup|quasinormal subgroup]], and others. See [[Groupprops:Category:Variations of normality]], [[Groupprops:Category:Opposites of normality]], and [[Groupprops:Category:Analogues of normality]].

Primary subject wiki entry: [[Groupprops:Normal subgroup]]

Other subject wiki entries: [[Diffgeom:Normal subgroup]]

Also located at: [[Wikipedia:Normal subgroup]], [[Planetmath:NormalSubgroup]], [[Mathworld:NormalSubgroup]], [[Sor:N/n067690]], [[Citizendium::Normal subgroup]]