Quotient-pullbackable automorphism

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 * quotient-pullbackable equals inner: A proof that every quotient-pullbackable automorphism of a group is an inner automorphism. An automorphism $$\sigma$$ of a group $$G$$ is termed a quoitent-pullbackable automorphism if for every group $$K$$ and surjective homomorphism $$\rho:K \to G$$ there exists an automorphism $$\sigma'$$ of $$K$$ such that $$\rho \circ \sigma' = \sigma \circ \rho$$.
 * 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.