Coprime automorphism-invariant subgroup of group of prime power order

Definition
A subgroup $$H$$ of a group of prime power order (i.e., a finite $$p$$-group for some prime number $$p$$) $$P$$ is termed a coprime automorphism-invariant subgroup if it is invariant under all the $$p'$$-automorphisms, i.e., the automorphisms whose order is relatively prime to $$p$$.

Stronger properties

 * Weaker than::Characteristic subgroup of group of prime power order
 * Weaker than::Coprime automorphism-invariant normal subgroup of group of prime power order
 * Weaker than::Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order
 * Weaker than::Sylow-relatively weakly closed subgroup
 * Weaker than::Fusion system-relatively weakly closed subgroup