Derived sub-IAPS

Definition
The derived sub-IAPS of an IAPS of groups is the sub-IAPS that, for the $$n^{th}$$ member, gives the derived subgroup (viz, commutator subgroup) of the $$n^{th}$$ member of the original IAPS.

The derived sub-IAPS need not be saturated. Hence, the quotient need not be an IAPS, and may simply be an APS.