# Category:Group Direct Products

This category contains results about Group Direct Products.
Definitions specific to this category can be found in Definitions/Group Direct Products.

Let $\struct {G, \circ_1}$ and $\struct {H, \circ_2}$ be groups.

Let $G \times H: \set {\tuple {g, h}: g \in G, h \in H}$ be their cartesian product.

The (external) direct product of $\struct {G, \circ_1}$ and $\struct {H, \circ_2}$ is the group $\struct {G \times H, \circ}$ where the operation $\circ$ is defined as:

$\tuple {g_1, h_1} \circ \tuple {g_2, h_2} = \tuple {g_1 \circ_1 g_2, h_1 \circ_2 h_2}$

This is usually referred to as the group direct product of $G$ and $H$.

## Subcategories

This category has the following 12 subcategories, out of 12 total.