Transfer-closed pronormal subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed transfer-closed pronormal if, for any subgroup $$K$$ of $$G$$, $$H \cap K$$ is a defining ingredient::pronormal subgroup of $$K$$.

Stronger properties

 * Weaker than::Hereditarily pronormal subgroup
 * Weaker than::Normal subgroup

Weaker properties

 * Stronger than::Pronormal subgroup