\begin{definition}[Definition:Group Direct Product/General Definition]
Let $\family {\struct {G_i, \circ_i} }_{i \mathop \in I}$ be a family of groups.
Let $\ds G = \prod_{i \mathop \in I} G_i$ be their cartesian product.
Let $\circ$ be the operation defined on $G$ as:
:$\circ := \family {g_i}_{i \mathop \in I} \circ \family {h_i}_{i \mathop \in I} = \family {g_i \circ_i h_i}_{i \mathop \in I}$
for all sequences in $G$.
The group $\struct {G, \circ}$  is called the '''(external) direct product''' of $\family {\struct {G_i, \circ_i} }_{i \mathop \in I}$.
Category:Definitions/Group Theory
Category:Definitions/Direct Products
\end{definition}