Subgroup in which every relatively normal subgroup is weakly closed

Symbol-free definition
A subgroup in which every relatively normal subgroup is weakly closed is a subgroup in which every defining ingredient::relatively normal subgroup (i.e., every subgroup that is normal inside the subgroup) is weakly closed.

Definition with symbols
A subgroup $$K$$ of a group $$G$$ is termed a subgroup in which every relatively normal subgroup is weakly closed if, for any subgroup $$H$$ of $$K$$ that is a normal subgroup of $$K$$ (not necessarily of $$G$$, $$H$$ is a defining ingredient::weakly closed subgroup in $$K$$ with respect to $$G$$.

Stronger properties

 * Weaker than::Abnormal subgroup
 * Weaker than::Transitively normal subgroup
 * Weaker than::CEP-subgroup
 * Weaker than::Retract
 * Weaker than::WNSCC-subgroup