Finite-quotient-pullbackable automorphism

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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Definition

Let G be a finite group and \sigma be an automorphism of G. We say that \sigma is a finite-quotient-pullbackable automorphism of G if, for any surjective homomorphism \rho:K \to G, there exists an automorphism \sigma' of K such that \rho \circ \sigma' = \sigma \circ \rho.

Relation with other properties

Weaker properties