I-simple IAPS

Symbol-free definition
An IAPS of groups is termed i-simple if it has no proper nontrivial saturated sub-IAPS. Equivalently, it is a simple object in the category of IAPSes with IAPS homomorphisms.

Stronger properties

 * Eventually simple IAPS

I-simple Abelian IAPSes
The only i-simple Abelian IAPSes are the power APSes over simple Abelian groups. The proof is direct.

I-simple non-Abelian IAPSes
I-simple non-Abelian IAPSes satisfy a similar principle as simple non-Abelian groups. Namely, any sub-IAPS-defining function on such a thing must either give a contrasaturated sub-IAPS, or the trivial sub-IAPS. This principle shows, in particular, that any i-simple IAPS is i-perfect.