Definition:Decomposable Group/Indecomposable

Definition

Let $\struct {G, \circ}$ be a group.

$\struct {G, \circ}$ is indecomposable if and only if it is not decomposable.

That is, if and only if there does not exist a decomposition of $\struct {G, \circ}$.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.16$