Group in which every p-local subgroup is of Glauberman type

Definition
Let $$G$$ be a finite group and $$p$$ be a prime number. We say that every p-local subgroup is of Glauberman type if every p-local subgroup (i.e., the normalizer of a non-identity $$p$$-subgroup) is a group of Glauberman type for the prime $$p$$.

Weaker properties

 * Stronger than::Group in which the ZJ-functor controls fusion: The proof follows by combining the fact that control of fusion is local and the fact that Glauberman type implies ZJ-functor controls fusion, which in turns follows from the fact that conjugacy functor whose normalizer generates whole group with p'-core controls fusion