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