Group property-conditionally 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 Group property-conditionally extensible automorphism, all facts related to Group property-conditionally 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

Suppose $\alpha$ is a group property and $G$ is a group satisfying $\alpha$. An automorphism $\sigma$ of $G$ is termed extensible with respect to $\alpha$, or extensible conditional to $\alpha$, if for any group $H$ containing $G$ such that $H$ satisfies property $\alpha$, there is an automorphism ${\sigma }^{\prime }$ of $H$ whose restriction to $G$ equals $\sigma$.

For more information on the best known results and characterization, refer extensible automorphisms problem.

When the groups satisfying $\alpha$ form a subvariety of the variety of groups, this is equivalent to the notion of variety-extensible automorphism for that subvariety.

Relation with other properties

Stronger properties

• Group property-conditionally pushforwardable automorphism

Related properties

• Group property-conditionally quotient-pullbackable automorphism

Other related notions

• Variety-extensible automorphism
• Own variety-extensible automorphism
• Extensibility operator
• Qualified extensibility operator