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- Extensible_automorphism abstract "In mathematics, an automorphism of a structure is said to be extensible if, for any embedding of that structure inside another structure, the automorphism can be lifted to the bigger structure. In group theory, an extensible automorphism of a group is an automorphism that can be lifted to an automorphism of any group in which it is embedded. A group automorphism is extensible if and only if it is an inner automorphism, (Schupp 1987).A times extensible automorphism of a group is defined inductively as an automorphism that can be lifted to a times extensible automorphism for any embedding, where a 0 times extensible automorphism is simply any automorphism. An automorphism that is times extensible for all is termed an extensible automorphism. The extensible automorphisms of a group form a subgroup for every .Here are some properties in increasing order of generality: The only extensible automorphism of an abelian group (extensible to arbitrary groups, not just to abelian groups) is the identity map. Every extensible automorphism of a finite group is an IA automorphism, that is, it acts as identity on the Abelianization. If a group has a homomorphic image acting on another group such that the other group is characteristic in the semidirect product and the homomorphic image is a central factor in its normalizer in the semidirect product then any extensible automorphism of the group must get quotiented to an inner automorphism of its homomorphic image.".
- Extensible_automorphism wikiPageID "5632354".
- Extensible_automorphism wikiPageRevisionID "450916205".
- Extensible_automorphism hasPhotoCollection Extensible_automorphism.
- Extensible_automorphism subject Category:Group_automorphisms.
- Extensible_automorphism subject Category:Group_theory.
- Extensible_automorphism comment "In mathematics, an automorphism of a structure is said to be extensible if, for any embedding of that structure inside another structure, the automorphism can be lifted to the bigger structure. In group theory, an extensible automorphism of a group is an automorphism that can be lifted to an automorphism of any group in which it is embedded.".
- Extensible_automorphism label "Extensible automorphism".
- Extensible_automorphism sameAs m.0dx9vk.
- Extensible_automorphism sameAs Q5421925.
- Extensible_automorphism sameAs Q5421925.
- Extensible_automorphism wasDerivedFrom Extensible_automorphism?oldid=450916205.
- Extensible_automorphism isPrimaryTopicOf Extensible_automorphism.