\begin{definition}[Definition:Internal Group Direct Product/General Definition]
Let $\sequence {H_n} = \struct {H_1, \circ {\restriction_{H_1} } }, \ldots, \struct {H_n, \circ {\restriction_{H_n} } }$ be a (finite) sequence of subgroups of a group $\struct {G, \circ}$
where $\circ {\restriction_{H_1} }, \ldots, \circ {\restriction_{H_n} }$ are the restrictions of $\circ$ to $H_1, \ldots, H_n$ respectively.
\end{definition}