Prime-extensible automorphism

Definition
Let $$p$$ be a prime. An automorphism of a group whose order is a power of $$p$$ is said to be $$p$$-extensible if for any embedding of the group in a bigger goup whose order is a power of the same prime, the automorphism can be extended to an automorphism of the bigger group.

Weaker properties

 * Finite-extensible automorphism (for a group of prime power order)

Related properties

 * Prime set-extensible automorphism