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- quotient-pullbackable equals inner: A proof that every quotient-pullbackable automorphism of a group is an inner automorphism. An automorphism of a group is termed a quoitent-pullbackable automorphism if for every group and surjective homomorphism there exists an automorphism of such that .
- group property-conditionally quotient-pullbackable automorphism: The property of being quotient-pullbackable within the collection of groups satisfying a particular property.
- variety-quotient-pullbackable automorphism
- extensible automorphisms problem: A discussion of this and related problems, and the current best known results.