Definition:Contranormal Subgroup

Definition
Let $G$ be a group.

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

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

Also see

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


 * Abnormal Subgroup is Contranormal Subgroup