\begin{definition}[Definition:Decomposable Group/Indecomposable]
Let $\left({G, \circ}\right)$ be a group.
$\left({G, \circ}\right)$ is '''indecomposable''' {{iff}} it is not decomposable.
That is, {{iff}} there does not exist a decomposition of $\left({G, \circ}\right)$.
\end{definition}