Absolutely normal subgroup

Definition
Suppose $$H \le K \le G$$ are groups. We say that $$H$$ is absolutely normal in $$K$$ with respect to $$G$$ if $$H$$ is a normal subgroup of $$G$$.

Weaker properties

 * Stronger than::Strongly closed subgroup
 * Stronger than::Weakly closed subgroup
 * Stronger than::Conjugation-invariantly relatively normal subgroup
 * Stronger than::Relatively normal subgroup