# Definition:Direct Product of Group Homomorphisms

## Theorem

Let $G, H_1$ and $H_2$ be groups.

Let $f_1: G \to H_1$ and $f_2: G \to H_2$ be group homomorphisms.

Then $f_1 \times f_2: G \to H_1 \times H_2$, defined as:

$\forall g \in G: \left({f_1 \times f_2}\right) \left({g}\right) = \left({f_1 \left({g}\right), f_2 \left({g}\right)}\right)$

is called the direct product of $f_1$ and $f_2$.