Maximal Sylow intersection

Definition
Let $$G$$ be a finite group and $$H$$ be a subgroup of $$G$$. Let $$p$$ be a prime number. We say that $$H$$ is a maximal $$p$$-Sylow intersection in $$G$$ if the following two conditions hold:


 * There exist two distinct $$p$$-Sylow subgroups $$P, Q$$ of $$G$$ such that $$H = P \cap Q$$.
 * For any two distinct $$p$$-Sylow subgroups $$R, S$$ of $$G$$, the order of $$R \cap S$$ is not more than the order of $$H$$.

Stronger properties

 * Weaker than::Sylow intersection of prime index

Weaker properties

 * Stronger than::Well-placed tame Sylow intersection
 * Stronger than::Tame Sylow intersection
 * Stronger than::Sylow intersection

Facts

 * Congruence condition on Sylow numbers in terms of maximal Sylow intersection