P-simple IAPS

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This term is related to: APS theory
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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 $(G,\Phi )$ is termed p-simple if there is no sub-IAPS $H$ of $G$ satisfying all these conditions:

• $H_{n}\triangleleft G_{n}$ 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