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

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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Definition

Let $G$ be a finite group and $p$ be a prime number. We say that $G$ is a group in which every p-local subgroup is p-solvable if every p-local subgroup of $G$ (i.e., the normalizer of any nonidentity $p$-subgroup) is a p-solvable group.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
N-group	This is a group in which every local subgroup is a solvable group.	Follows from the fact that p-local implies local and solvable implies p-solvable
group in which every p-local subgroup is strongly p-solvable	We replace the p-solvable group condition by a strongly p-solvable group condition. For $p\geq 5$, the definitions are equivalent.

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
group in which every p-local subgroup is p-constrained
(for $p\geq 5$): group in which every p-local subgroup is of Glauberman type
(for $p\geq 5$): group in which the ZJ-functor controls fusion		(via group in which every p-local subgroup is of Glauberman type for p)