# Group property-conditionally quotient-pullbackable automorphism

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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 is a group property and is a group satisfying . An automorphism of is termed **quotient-pullbackable** with respect to , or quotient-pullbackable conditional to , if for any group and surjective homomorphism such that satisfies property , there is an automorphism of such that .

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

When the groups satisfying form a subvariety of the variety of groups, this is equivalent to the notion of variety-quotient-pullbackable automorphism for that subvariety.

Also note that any inner automorphism is conditionally quotient-pullbackable with respect to any group property.