# Difference between revisions of "Normal subgroup"

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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. | ||

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

## Revision as of 16:23, 14 May 2008

**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), normal core (the largest normal subgroup contained in a given subgroup), normal closure (the smallest normal subgroup containing a given subgroup), normalizer (the largest subgroup containing a given subgroup, in which it is normal).

Term variations: subnormal subgroup, abnormal 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