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- Conjugacy-closed_subgroup abstract "In mathematics, in the field of group theory, a subgroup of a group is said to be conjugacy-closed if any two elements of the subgroup that are conjugate in the group are also conjugate in the subgroup.An alternative characterization of conjugacy-closed normal subgroups is that all class automorphisms of the whole group restrict to class automorphisms of the subgroup.The following facts are true regarding conjugacy-closed subgroups: Every central factor (a subgroup that may occur as a factor in some central product) is a conjugacy-closed subgroup. Every conjugacy-closed normal subgroup is a transitively normal subgroup. The property of being conjugacy-closed is transitive, that is, every conjugacy-closed subgroup of a conjugacy-closed subgroup is conjugacy-closed.The property of being conjugacy-closed is sometimes also termed as being conjugacy stable. It is a known result that for finite field extensions, the general linear group of the base field is a conjugacy-closed subgroup of the general linear group over the extension field. This result is typically referred to as a stability theorem.A subgroup is said to be strongly conjugacy-closed if all intermediate subgroups are also conjugacy-closed.".
- Conjugacy-closed_subgroup wikiPageExternalLink Central_factor.
- Conjugacy-closed_subgroup wikiPageExternalLink Conjugacy-closed_subgroup.
- Conjugacy-closed_subgroup wikiPageID "4978117".
- Conjugacy-closed_subgroup wikiPageLength "1742".
- Conjugacy-closed_subgroup wikiPageOutDegree "12".
- Conjugacy-closed_subgroup wikiPageRevisionID "669255049".
- Conjugacy-closed_subgroup wikiPageWikiLink Category:Subgroup_properties.
- Conjugacy-closed_subgroup wikiPageWikiLink Central_product.
- Conjugacy-closed_subgroup wikiPageWikiLink Class_automorphism.
- Conjugacy-closed_subgroup wikiPageWikiLink Conjugacy_class.
- Conjugacy-closed_subgroup wikiPageWikiLink Field_extension.
- Conjugacy-closed_subgroup wikiPageWikiLink General_linear_group.
- Conjugacy-closed_subgroup wikiPageWikiLink Group_(mathematics).
- Conjugacy-closed_subgroup wikiPageWikiLink Group_theory.
- Conjugacy-closed_subgroup wikiPageWikiLink Mathematics.
- Conjugacy-closed_subgroup wikiPageWikiLink Normal_subgroup.
- Conjugacy-closed_subgroup wikiPageWikiLink Subgroup.
- Conjugacy-closed_subgroup wikiPageWikiLink Transitively_normal_subgroup.
- Conjugacy-closed_subgroup wikiPageWikiLinkText "Conjugacy-closed subgroup".
- Conjugacy-closed_subgroup hasPhotoCollection Conjugacy-closed_subgroup.
- Conjugacy-closed_subgroup wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Conjugacy-closed_subgroup wikiPageUsesTemplate Template:Orphan.
- Conjugacy-closed_subgroup wikiPageUsesTemplate Template:Unreferenced.
- Conjugacy-closed_subgroup subject Category:Subgroup_properties.
- Conjugacy-closed_subgroup hypernym Conjugate.
- Conjugacy-closed_subgroup type Drug.
- Conjugacy-closed_subgroup comment "In mathematics, in the field of group theory, a subgroup of a group is said to be conjugacy-closed if any two elements of the subgroup that are conjugate in the group are also conjugate in the subgroup.An alternative characterization of conjugacy-closed normal subgroups is that all class automorphisms of the whole group restrict to class automorphisms of the subgroup.The following facts are true regarding conjugacy-closed subgroups: Every central factor (a subgroup that may occur as a factor in some central product) is a conjugacy-closed subgroup. ".
- Conjugacy-closed_subgroup label "Conjugacy-closed subgroup".
- Conjugacy-closed_subgroup sameAs m.0cy3xy.
- Conjugacy-closed_subgroup sameAs Q5015126.
- Conjugacy-closed_subgroup sameAs Q5015126.
- Conjugacy-closed_subgroup wasDerivedFrom Conjugacy-closed_subgroup?oldid=669255049.
- Conjugacy-closed_subgroup isPrimaryTopicOf Conjugacy-closed_subgroup.