Cocentral subgroup of normalizer

Symbol-free definition
A subgroup of a group is said to be a cocentral subgroup of normalizer if it is a cocentral subgroup of its normalizer.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is said to be a cocentral subgroup of normalizer if $$HZ(N_G(H)) = N_G(H)$$ where $$Z(N_G(H))$$ denotes the center of $$N_G(H)$$ and $$N_G(H)$$ denotes the normalizer of $$H$$.

Stronger properties

 * Weaker than::Cocentral subgroup
 * Weaker than::Weakly cocentral subgroup
 * Weaker than::Self-normalizing subgroup

Weaker properties

 * Stronger than::Central factor of normalizer