Constant APS of an abelian group

Definition
Let $$G$$ be an defining ingredient::abelian group. The constant APS of $$G$$ is an APS whose $$n^{th}$$ member is $$G$$, and where the concatenation map $$\Phi_{m,n}$$ is the group operation.

The constant APS is an APS of groups but is not an IAPS of groups.