Join-transitively pronormal subgroup

Symbol-free definition
A subgroup of a group is termed join-transitively pronormal if its join with any pronormal subgroup of the group is pronormal.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed join-transitively pronormal if, for any pronormal subgroup $$K$$ of $$G$$, the join $$\langle H, K \rangle$$ is also pronormal.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::Abnormal subgroup
 * Weaker than::Weakly abnormal subgroup
 * Weaker than::Upward-closed pronormal subgroup

Weaker properties

 * Stronger than::Pronormal subgroup