I-simple IAPS

From Apstheory

Contents 1 Definition 1.1 Symbol-free definition 2 Definition 2.1 Relation with other forms of simplicity

Definition

Symbol-free definition

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

Definition

Relation with other forms of simplicity

i-simplicity is among the weakest notions of simplicity. Any p-simple IAPS, and hence any eventually simple IAPS, is i-simple.