Given a subgroup $\displaystyle A \subseteq G$, consider the set $\displaystyle N_G(A) = \{g \in G | gAg^{-1} = A\}$.
Prove that $\displaystyle A$ is normal if and only if $\displaystyle N_G(A) = G$.
Given a subgroup $\displaystyle A \subseteq G$, consider the set $\displaystyle N_G(A) = \{g \in G | gAg^{-1} = A\}$.
Prove that $\displaystyle A$ is normal if and only if $\displaystyle N_G(A) = G$.