Local subgroup for a prime

Symbol-free definition
Let $$p$$ be a prime. A subgroup of a group is said to be a $$p$$-local subgroup if it occurs as the normalizer of a $$p$$-subgroup.

Definition with symbols
Let $$p$$ be a prime. A subgroup $$H$$ of a group $$G$$ is said to be a $$p$$-local subgroup if there exists a $$p$$-subgroup $$Q$$ such that $$H = N_G(Q)$$.

Stronger properties

 * Local subgroup

Weaker properties

 * Sylow-normalizer