Nilpotent-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 term is related to: Extensible automorphisms problem
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Definition

Symbol-free definition

An automorphism of a nilpotent group is said to be nilpotent-extensible if it can be extended to an automorphism for every embedding of the given nilpotent group into a nilpotent group.

Definition with symbols

Let $G$ be a nilpotent group and $\sigma$ an automorphism of $G$. Then we say that $\sigma$ is nilpotent-extensible if for any embedding of $G$ in a nilpotent group $H$, there is an automorphism $\phi$ of $H$ such that the restriction of $\phi$ to $G$ is $\sigma$.

Relation with other properties

Stronger properties

• Extensible automorphism when the underlying group is nilpotent
• Solvable-extensible automorphism when the underlying group is nilpotent