Definition:Decomposable Group

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

Then $\struct {G, \circ}$ is decomposable if and only if there exists a decomposition of $\struct {G, \circ}$.

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


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

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

Also see

  • Results about decomposable groups can be found here.