Subgroup with canonical abelianization: Difference between revisions
(New page: {{wikilocal}} {{subgroup property}} ==Definition== A '''subgroup with canonical Abelianization''' is a subgroup satisfying the following property: any [[defining ingredient::inner automo...) |
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A '''subgroup with canonical Abelianization''' is a subgroup satisfying the following property: any [[defining ingredient::inner automorphism]] of the whole group that sends the subgroup to itself, restricts to an [[defining ingredient::IA-automorphism]] of the subgroup. | A '''subgroup with canonical Abelianization''' is a subgroup satisfying the following property: any [[defining ingredient::inner automorphism]] of the whole group that sends the subgroup to itself, restricts to an [[defining ingredient::IA-automorphism]] of the subgroup. | ||
==Formalisms== | |||
{{obtainedbyapplyingthe|in-normalizer operator|IA-balanced subgroup}} | |||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 19:54, 24 September 2008
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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition
A subgroup with canonical Abelianization is a subgroup satisfying the following property: any inner automorphism of the whole group that sends the subgroup to itself, restricts to an IA-automorphism of the subgroup.
Formalisms
In terms of the in-normalizer operator
This property is obtained by applying the in-normalizer operator to the property: IA-balanced subgroup
View other properties obtained by applying the in-normalizer operator