# Math Help - Normalizer as a subgroup. Unique largest subgroup in which A is normal.

1. ## Normalizer as a subgroup. Unique largest subgroup in which A is normal.

Prove that the normalizer of $A \subseteq G$ is always a subgroup of $G$ which contains $A$. Further prove it is the unique largest subgroup in which $A$ is normal.

2. Originally Posted by joestevens
Prove that the normalizer of $A \subseteq G$ is always a subgroup of $G$ which contains $A$. Further prove it is the unique largest subgroup in which $A$ is normal.
What particularly are you having trouble with?

3. Originally Posted by Drexel28
What particularly are you having trouble with?
Am I supposed to show $A \subseteq N(A) \subseteq G$ or just that $N(A) \subseteq G$, when $A \subseteq G$?
Where should I start?