Hall-semidirectly extensible automorphism

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This term is related to: Extensible automorphisms problem
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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 ${\sigma }^{\prime }$ 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