Relatively normal subgroup

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

Stronger properties

 * Weaker than::Absolutely normal subgroup
 * Weaker than::Strongly closed subgroup
 * Weaker than::Weakly closed subgroup
 * Weaker than::Conjugation-invariantly relatively normal subgroup