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 be a group of prime power order, i.e., a finite -group for some prime . An automorphism of is termed a p-quotient-pullbackable automorphism if, given any finite -group and a surjective homomorphism , there exists an automorphism of that is a pullback of ; in other words, .
Relation with other properties
- Inner automorphism of a finite -group.
- Cofactorial automorphism: Any -quotient-pullbackable automorphism of a finite -group is itself a -automorphism. For full proof, refer: p-quotient-pullbackable automorphism implies p-automorphism
- p-quotient-pullbackable automorphism of elementary abelian group is trivial: This is an immediate corollary of Bryant-Kovacs theorem.