Definition:Contranormal Subgroup

Definition
Let $G$ be a group.

Let $H$ be a subgroup of $G$.

Then $H$ is a contranormal subgroup iff the normal closure of $H$ is the whole of $G$.

Also see

 * Normal Subgroup
 * Subnormal Subgroup
 * Abnormal Subgroup
 * Weakly Abnormal Subgroup
 * Self-Normalizing Subgroup
 * Pronormal Subgroup
 * Weakly Pronormal Subgroup
 * Paranormal Subgroup
 * Polynormal Subgroup


 * Abnormal Subgroup is Contranormal Subgroup