## Fundamental Theorem of Finitely Generated Abelian Groups and its application

## Problem 420

In this post, we study the **Fundamental Theorem of Finitely Generated Abelian Groups**, and as an application we solve the following problem.

**Problem**.

Let $G$ be a finite abelian group of order $n$.

If $n$ is the product of distinct prime numbers, then prove that $G$ is isomorphic to the cyclic group $Z_n=\Zmod{n}$ of order $n$.