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- Fully_normalized_subgroup abstract "In mathematics, in the field of group theory, a subgroup of a group is said to be fully normalized if every automorphism of the subgroup lifts to an inner automorphism of the whole group. Another way of putting this is that the natural embedding from the Weyl group of the subgroup to its automorphism group is surjective.In symbols, a subgroup is fully normalized in if, given an automorphism of , there is a such that the map , when restricted to is equal to .Some facts: Every group can be embedded as a normal and fully normalized subgroup of a bigger group. A natural construction for this is the holomorph, which is its semidirect product with its automorphism group. A complete group is fully normalized in any bigger group in which it is embedded because every automorphism of it is inner. Every fully normalized subgroup has the automorphism extension property.".
- Fully_normalized_subgroup wikiPageID "4966995".
- Fully_normalized_subgroup wikiPageRevisionID "601707864".
- Fully_normalized_subgroup hasPhotoCollection Fully_normalized_subgroup.
- Fully_normalized_subgroup subject Category:Group_theory.
- Fully_normalized_subgroup subject Category:Subgroup_properties.
- Fully_normalized_subgroup type Abstraction100002137.
- Fully_normalized_subgroup type Possession100032613.
- Fully_normalized_subgroup type Property113244109.
- Fully_normalized_subgroup type Relation100031921.
- Fully_normalized_subgroup type SubgroupProperties.
- Fully_normalized_subgroup comment "In mathematics, in the field of group theory, a subgroup of a group is said to be fully normalized if every automorphism of the subgroup lifts to an inner automorphism of the whole group.".
- Fully_normalized_subgroup label "Fully normalized subgroup".
- Fully_normalized_subgroup sameAs m.0cxkw_.
- Fully_normalized_subgroup sameAs Q5508345.
- Fully_normalized_subgroup sameAs Q5508345.
- Fully_normalized_subgroup sameAs Fully_normalized_subgroup.
- Fully_normalized_subgroup wasDerivedFrom Fully_normalized_subgroup?oldid=601707864.
- Fully_normalized_subgroup isPrimaryTopicOf Fully_normalized_subgroup.