P-simple IAPS

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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 (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

Weaker properties