Coprime automorphism-invariant normal subgroup

Definition
A subgroup of a finite group is termed a coprime automorphism-invariant normal subgroup if it is both normal and coprime automorphism-invariant: it is invariant under all coprime automorphisms of the whole group.

Stronger properties

 * Weaker than::Isomorph-normal coprime automorphism-invariant subgroup

Weaker properties

 * Stronger than::Normal subgroup
 * Stronger than::Coprime automorphism-invariant subgroup

Facts

 * Coprime automorphism-invariant normal subgroup of Hall subgroup is normalizer-relatively normal
 * Coprime automorphism-invariant normal of normal Hall implies normal
 * Left residual of normal by normal Hall is coprime automorphism-invariant normal
 * Hall-relatively weakly closed implies coprime automorphism-invariant normal