P-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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Let P be a group of prime power order, i.e., a finite p-group for some prime p. An automorphism \sigma of P is termed a p-quotient-pullbackable automorphism if, given any finite p-group Q and a surjective homomorphism \rho:Q \to P, there exists an automorphism \sigma' of Q that is a pullback of \sigma; in other words, \rho \circ \sigma' = \sigma \circ \rho.

Relation with other properties

Stronger properties

Weaker properties