Definition:Decomposable Group

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Definition

Let $\left({G, \circ}\right)$ be a group.

Then $\left({G, \circ}\right)$ is decomposable if and only if there exists a decomposition of $\left({G, \circ}\right)$.

That is, if and only if $\left({G, \circ}\right)$ is the internal direct product of two (or more) proper subgroups of $G$.


Indecomposable

$\left({G, \circ}\right)$ is indecomposable if and only if it is not decomposable.

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


Sources