Definition:Self-Normalizing Subgroup

Definition
Let $G$ be a group.

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

Then $H$ is a self-normalizing subgroup iff:


 * $N_G \left({H}\right) = H$

where $N_G \left({H}\right)$ is the normalizer of $H$ in $G$.

Also see

 * Definition:Normal Subgroup
 * Definition:Subnormal Subgroup
 * Definition:Abnormal Subgroup
 * Definition:Weakly Abnormal Subgroup
 * Definition:Contranormal Subgroup
 * Definition:Pronormal Subgroup
 * Definition:Weakly Pronormal Subgroup
 * Definition:Paranormal Subgroup
 * Definition:Polynormal Subgroup


 * Abnormal Subgroup is Self-Normalizing Subgroup
 * Weakly Abnormal Subgroup is Self-Normalizing Subgroup