Finite-upper join-closed subgroup property

Definition
A subgroup property $$p$$ is termed a finite-upper join-closed subgroup property if, for any subgroup $$H$$ of a group $$G$$, and any intermediate subgroups $$K_1, K_2$$ of $$G$$ such that $$H$$ satisfies $$p$$ in both $$K_1$$ and $$K_2$$, we have that $$H$$ satisfies $$p$$ in the defining ingredient::join of subgroups $$\langle K_1, K_2 \rangle$$.

Stronger metaproperties

 * Weaker than::Upper join-closed subgroup property

Weaker metaproperties

 * Stronger than::Permuting upper join-closed subgroup property