Abnormal Subgroup is Self-Normalizing Subgroup

Theorem

Let $G$ be a group.

Let $H$ be an abnormal subgroup of $G$.

Then $H$ is a self-normalizing subgroup of $G$.

Proof

We have:

• Abnormal Subgroup is Weakly Abnormal Subgroup
• Weakly Abnormal Subgroup is Self-Normalizing Subgroup

Hence the result.

$\blacksquare$