Weakly cocentral subgroup

Symbol-free definition
A subgroup of a group is termed weakly cocentral if its product with the center of the group contains its normalizer.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed weakly cocentral if $$N_G(H) \le HZ(G)$$.

Stronger properties

 * Cocentral subgroup where we require the product with the center to be the whole group
 * Self-normalizing subgroup where we require the subgroup to itself equal its normalizer

Weaker properties

 * Stronger than::Double coset-separated subgroup
 * Stronger than::Cocentral subgroup of normalizer
 * Stronger than::Central factor of normalizer