\begin{definition}[Definition:Decomposable Group]
Let $\left({G, \circ}\right)$ be a group.
Then $\left({G, \circ}\right)$ is '''decomposable''' {{iff}} there exists a decomposition of $\left({G, \circ}\right)$.
That is, {{iff}} $\left({G, \circ}\right)$ is the internal direct product of two (or more) proper subgroups of $G$.
\end{definition}