# Category:Examples of Group Direct Products

Jump to navigation
Jump to search

This category contains examples of **Group Direct Product**.

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 $H$.

## Pages in category "Examples of Group Direct Products"

The following 7 pages are in this category, out of 7 total.

### G

- Group Direct Product/Examples
- Group Direct Product/Examples/C2 x C2
- Group Direct Product/Examples/C2 x C2/Subgroups
- Group Direct Product/Examples/C2 x C3
- Group Direct Product/Examples/C3 x C3
- Group Direct Product/Examples/R-0 x R
- Group Direct Product/Examples/R-0 x R/Isomorphism to Set of Affine Mappings on Real Line under Composition