Definition:Self-Normalizing Subgroup

Definition

Let $G$ be a group.

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

Then $H$ is a self-normalizing subgroup if and only if:

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

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

• Results about self-normalizing subgroups can be found here.