CS-extensible automorphism

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |
This term is related to: Extensible automorphisms problem
View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Symbol-free definition

An automorphism of a group is termed CS-extensible if it can be extended to an inner automorphism for every embedding of the group into the automorphism group of a characteristically simple group.

Definition with symbols

Let G be a group and \sigma an automorphism of G. We say that \sigma is CS-extensible if for any embedding G \le Aut(N) where N is a characteristically simple group, there is an inner automorphism \phi of Aut(N) such that the restriction of \phi to G is \sigma.

Relation with other properties

Stronger properties