Permuting join-closed subgroup property

Definition
A subgroup property $$p$$ is termed a permuting join-closed subgroup property if, for any group $$G$$ and permuting subgroups $$H$$ and $$K$$ of $$G$$ such that $$H$$ and $$K$$ both satisfy $$p$$ in $$G$$, we must have that $$HK$$ satisfies $$p$$ in $$G$$.

Stronger metaproperties

 * Weaker than::Strongly join-closed subgroup property
 * Weaker than::Join-closed subgroup property
 * Weaker than::Strongly finite-join-closed subgroup property
 * Weaker than::Finite-join-closed subgroup property

Weaker metaproperties

 * Stronger than::Normalizing join-closed subgroup property