Strongly closed subgroup for a fusion system

Definition
Let $$P$$ be a group of prime power order and $$\mathcal{F}$$ be a fusion system for $$P$$. A subgroup $$Q$$ of $$P$$ is termed strongly closed with respect to $$\mathcal{F}$$, if given any subgroup $$R \le P$$, and any morphism $$\varphi$$ in $$\mathcal{F}$$ from $$R$$ to $$P$$, we have:

$$\varphi(R \cap Q) \le Q$$

Weaker properties

 * Weakly closed subgroup for a fusion system