P-simple IAPS

This term is related to: APS theory
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ANALOGY: This is an analogue in IAPSs of the group property:
View other analogues of simple group | View other analogues in IAPSs of group properties

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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 $(G,\mathrm{\Phi })$ is termed p-simple if there is no sub-IAPS $H$ of $G$ satisfying all these conditions:

• $H_n◃G_n$ for every $n$
• There are infinitely many indices $n$ for which $H_n$ is properly contained in $G_n$
• $H_n$ is nontrivial for at least some value of $n$

Relation with other properties

Stronger properties

• Eventually simple IAPS

Weaker properties

• i-simple IAPS