# P-simple IAPS

From Groupprops

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

This term is related to: APS theory

View other terms related to APS theory | View facts related to APS theory

ANALOGY: This is an analogue in IAPS of a property encountered in group. Specifically, it is a IAPS property analogous to the group property: simple group

View other analogues of simple group | View other analogues in IAPSs of group properties (OR, View as a tabulated list)

*This article defines a property that can be evaluated for an IAPS of groups*

## Definition

### Symbol-free definition

An IAPS of groups is termed **p-simple** if it has no strongly proper nontrivial normal sub-IAPS.

### Definition with symbols

An IAPS of groups is termed **p-simple** if there is no sub-IAPS of satisfying all these conditions:

- for every
- There are infinitely many indices for which is properly contained in
- is nontrivial for at least some value of