CS-extensible automorphism

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
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Definition

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 $G\leq Aut(N)$ 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

• Extensible automorphism
• Semidirectly extensible automorphism
• Potentially characteristic-semidirectly extensible automorphism
• CS-pushforwardable automorphism