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:

$\forall g \in G: \map{\paren {f_1 \times f_2} } g = \tuple {\map {f_1} g, \map {f_2} g}$

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

Also see

• Direct Product of Group Homomorphisms is Homomorphism

Sources

• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Direct Products