en>K9re11: removed Category:Group theory using HotCat as there are already more specific subcategories

2014-11-15T20:37:05Z

removed Category:Group theory using HotCat as there are already more specific subcategories

← Older revision		Revision as of 22:37, 15 November 2014
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	~~In [[mathematics]],~~ in ~~the field of [[group theory]],~~ a ~~[[subgroup]] of a [[group (mathematics)\|group]]~~ is ~~said to have the~~ '~~''Congruence Extension Property''' or to be a '''CEP subgroup''' if every [[congruence relation\|congruence]] on the subgroup lifts to a congruence of the whole group~~. ~~Equivalently, every [[normal subgroup]] of the subgroup arises as the intersection with the subgroup of a normal subgroup of the whole group.~~		Hello buddy. Allow me introduce myself. I am Luther Aubrey. I've always loved living in Idaho. My job is a messenger. Camping is something that I've carried out for years.<br><br>Feel free to surf to my weblog - [http://titon.net/UserProfile/tabid/43/userId/160343/Default.aspx titon.net]

	~~In symbols, a subgroup~~ <~~math~~>H</~~math> is normal in a group <math>G<~~/~~math> if every normal subgroup <math>N<~~/~~math> of <math>H<~~/~~math> can be realized as <math>H \cap M<~~/~~math> where <math>M<~~/~~math> is normal in <math>G<~~/~~math>~~.

	~~The following facts are known about CEP subgroups:~~

	* Every [[retract (group theory)\|retract]] has the CEP.
	* Every [[transitively normal subgroup]~~] has the CEP.~~

	~~[[Category:Group theory]]~~
	~~[[Category:Subgroup properties]]~~


	~~{{Abstract-algebra-stub}}~~

en>Qetuth: more specific stub type + added reference

2012-01-01T11:01:43Z

more specific stub type + added reference

New page

In [[mathematics]], in the field of [[group theory]], a [[subgroup]] of a [[group (mathematics)|group]] is said to have the '''Congruence Extension Property''' or to be a '''CEP subgroup''' if every [[congruence relation|congruence]] on the subgroup lifts to a congruence of the whole group. Equivalently, every [[normal subgroup]] of the subgroup arises as the intersection with the subgroup of a normal subgroup of the whole group.

In symbols, a subgroup <math>H</math> is normal in a group <math>G</math> if every normal subgroup <math>N</math> of <math>H</math> can be realized as <math>H \cap M</math> where <math>M</math> is normal in <math>G</math>.

The following facts are known about CEP subgroups:

* Every [[retract (group theory)|retract]] has the CEP.
* Every [[transitively normal subgroup]] has the CEP.

[[Category:Group theory]]
[[Category:Subgroup properties]]

{{Abstract-algebra-stub}}

Strictly simple group - Revision history

en>K9re11: removed Category:Group theory using HotCat as there are already more specific subcategories

en>Qetuth: more specific stub type + added reference