\begin{remark}[Greedy Algorithm for an Abelian Group of Order $\mathbf{p^n}$] The Fundamental Theorem is extremely powerful. As an application, we can use it as an ...

Let $\phi$ be a group homomorphism from $G$ to $\overline{G}$. Then the mapping from $G/\ker\phi$ to $\phi(G)$, given by $g\ker\phi \to \phi(g)$, is an isomorphism ...