 Direct product of groups

The direct product $G\times H$ has componentwise multiplication. An element $(g,h)$ of finite component orders has order $\mathrm{lcm}(\mathrm{ord}g,\mathrm{ord}h)$.

In group theory, the **direct product** (also known as the **Cartesian product** or **product group**) of two groups combines the two groups into a new group. Here's a detailed explanation: ### Definition: Let \( G \) and \( H \) be two groups.