Group in which every p-local subgroup is p-constrained

Statement
Suppose $$G$$ is a finite group and $$p$$ is a prime number. We say that $$G$$ is a group in which every p-local subgroup is p-constrained if any $$p$$-local subgroup (i.e., the normalizer of any non-identity $$p$$-subgroup) of $$G$$ is a defining ingredient::p-constrained group.

Facts

 * Thompson transitivity theorem
 * Lemma on containment in p'-core for Thompson transitivity theorem