Strongly closed conjugacy functor

Definition
Suppose $$G$$ is a finite group, $$p$$ is a prime number, and $$W$$ is a conjugacy functor for the prime $$p$$. We say that $$W$$ is a strongly closed conjugacy functor if it satisfies the following equivalent conditions:


 * There exists a $$p$$-Sylow subgroup $$P$$ of $$G$$ such that $$W(P)$$ is a defining ingredient::strongly closed subgroup of $$P$$ relative to $$G$$.
 * For every $$p$$-Sylow subgroup $$P$$ of $$G$$, $$W(P)$$ is a strongly closed subgroup of $$P$$ relative to $$G$$.