Stem extension - Revision history

Vipul at 19:41, 8 May 2013

2013-05-08T19:41:13Z

← Older revision		Revision as of 19:41, 8 May 2013
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	* [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s.		* [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s.

			==Relation with other properties==

			===Weaker properties of group extensions===

			* [[weak stem extension]]
			* [[central extension]]
	==Facts==		==Facts==

	* [[Base of stem extension need not be the whole center]]		* [[Base of stem extension need not be the whole center]]

Vipul at 23:20, 14 December 2011

2011-12-14T23:20:06Z

← Older revision		Revision as of 23:20, 14 December 2011
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	* [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s.		* [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s.

			==Facts==

			* [[Base of stem extension need not be the whole center]]

Vipul at 01:45, 1 November 2011

2011-11-01T01:45:12Z

← Older revision		Revision as of 01:45, 1 November 2011
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	==Definition==		==Definition==

	A ''stem extension''' is a [[defining ingredient::group extension]] where the base [[normal subgroup]] is contained in both the [[defining ingredient::center]] and the [[defining ingredient::derived subgroup]] of the whole group.		A '''stem extension''' is a [[defining ingredient::group extension]] where the base [[normal subgroup]] is contained in both the [[defining ingredient::center]] and the [[defining ingredient::derived subgroup]] of the whole group.

	In particular, it is a special kind of [[defining ingredient::central extension]].		In particular, it is a special kind of [[defining ingredient::central extension]].

Vipul at 01:44, 1 November 2011

2011-11-01T01:44:55Z

← Older revision		Revision as of 01:44, 1 November 2011
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	==Definition==		==Definition==

	~~===Definition with symbols===~~		A ''stem extension''' is a [[defining ingredient::group extension]] where the base [[normal subgroup]] is contained in both the [[defining ingredient::center]] and the [[defining ingredient::derived subgroup]] of the whole group.

	~~A ''stem extension''' of a [[group]] <math>G</math>~~ is a ~~group <math>E</math> along with a surjective homomorphism <math>\rho:E \to G</math> such that the kernel of <math>\rho</math> is contained in the [[intersection of subgroups\|intersection]]~~ of ~~the~~ [[defining ingredient::~~center~~]] ~~and the [[defining ingredient::derived subgroup]] of <math>E</math>~~.		In particular, it is a special kind of [[defining ingredient::central extension]].

	A stem extension ~~is a particular kind~~ of [[~~defining ingredient::~~central extension]].		==Related notions==

			* [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s.

Vipul: Created page with '==Definition== ===Definition with symbols=== A ''stem extension''' of a group $G$ is a group $E$ along with a surjective homomorphism $\rho:E \to…'$

2010-04-14T22:38:53Z

Created page with '==Definition== ===Definition with symbols=== A ''stem extension''' of a group <math>G</math> is a group <math>E</math> along with a surjective homomorphism <math>\rho:E \to…'

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