Normal subgroup: Difference between revisions

Latest revision as of 12:30, 29 December 2009

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), normal automorphism (an automorphism that restricts to an automorphism on every normal subgroup).

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. See also Groupprops:Questions: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, Springer Online Reference Works, Citizendium: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.
-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]].
-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]]
+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]]