Group property-conditionally quotient-pullbackable automorphism
This term is related to: extensible automorphisms problem
View other terms related to extensible automorphisms problem | View facts related to extensible automorphisms problem
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.