# Thread: Number of group homomorphisms

1. ## Number of group homomorphisms

My solution to this problem, although it can be generalized to any finite abelian group $G$, is not straightforward. See if you can find a simple solution:

Let $p$ be a prime number. Let $G_1$ and $G_2$ be cyclic groups of orders $p$ and $p^2$ respectively. Let $G=G_1 \times G_2.$ Find the number of group homomorphisms $f: G \longrightarrow G.$