Sylow intersection

Definition with symbols
Let $$G$$ be a finite group and $$p$$ be a prime number. A subgroup $$H$$ of $$G$$ is termed a $$p$$-Sylow intersection if it satisfies the following equivalent conditions:


 * $$H$$ can be expressed as $$P \cap Q$$ for two distinct $$p$$-Sylow subgroups $$P, Q$$ of $$G$$.
 * $$H$$ can be expressed as $$P \cap N_G(Q)$$ for two distinct $$p$$-Sylow subgroups $$P,Q$$ of $$G$$.

A subgroup is termed a Sylow intersection if it is a $$p$$-Sylow intersection for some $$p$$.

Stronger properties

 * Weaker than::Tame Sylow intersection
 * Weaker than::Maximal Sylow intersection

Weaker properties

 * Stronger than::Intersection of Sylow subgroups