Direct Product#
Definition: Direct Product
Let \((G_1, \cdot_1), \dotsc, (G_n, \cdot_n)\) be groups and let \(\mathcal{G}\) be their Cartesian product.
Their direct product is \(\mathcal{G}\) with the operation \(\cdot: \mathcal{G} \times \mathcal{G} \to \mathcal{G}\) defined in the following way:
\[ (a_1, \dotsc, a_n) \cdot (b_1, \dotsc, b_n) = (a_1 \cdot_1 b_1, \dotsc, a_n \cdot_n b_n) \]