Strictly simple group: Difference between revisions

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en>Qetuth
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en>K9re11
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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.
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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}}

Latest revision as of 21:37, 15 November 2014

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.

Feel free to surf to my weblog - titon.net

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