A subgroup $H$ of a group $G$ is said to be a characteristic subgroup if $\sigma(H) = H$ for every group isomorphism $\sigma : G \longrightarrow G$ of $G$.\\
(A) Determine all the characteristic subgroups of $(\mathbb{Q}, +)$ (the additive group).\\
(B) Show that every characteristic subgroup of $G$ is normal in $G$. Determine whether the converse is true.