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

The article defines a property of groups, where the definition may be in terms of a particular prime that serves as parameter
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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 p-constrained group.

Facts

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

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Group in which every p-local subgroup is p-solvable	every p-local subgroup is a p-solvable group (for that specific prime number $p$)	follows from p-solvable implies p-constrained		|FULL LIST, MORE INFO
N-group (finite)	every local subgroup (normalizer of a nontrivial solvable subgroup) is solvable			|FULL LIST, MORE INFO
minimal simple group (finite)	simple non-abelian group in which every proper subgroup is solvable			|FULL LIST, MORE INFO
p-solvable group
finite solvable group
p-nilpotent group
finite nilpotent group