Hall-semidirectly extensible automorphism

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

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Hall-semidirectly extensible automorphism, all facts related to Hall-semidirectly extensible automorphism) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

This term is related to: Extensible automorphisms problem
View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

Definition

Let $G$ be a finite group and $\sigma$ be an automorphism of $G$. $\sigma$ is termed Hall-semidirectly extensible if for every group $K$ containing <mah>G</math> as a Hall retract, i.e., containing $G$ as a Hall subgroup with a normal complement, there exists an automorphism $\sigma '$ of $K$ whose restriction to $G$ is $\sigma$.

Relation with other properties

Stronger properties

• Finite-characteristic-semidirectly extensible automorphism
• Hall-extensible automorphism

Weaker properties

• Class-preserving automorphism