Weakly cocentral subgroup

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Definition

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 $N_{G}(H)\leq HZ(G)$ .

Relation with other properties

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