I-simple IAPS
From Apstheory
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
| - | An [[IAPS of groups]] is termed '''i-simple''' if it has no [[proper sub-APS|proper]] [[nontrivial APS|nontrivial]] [[saturated sub-APS]] [[sub-IAPS]]. Equivalently, it is a simple object in the category of IAPSes with IAPS homomorphisms. | + | An [[IAPS of groups]] is termed '''i-simple''' if it has no [[proper sub-APS|proper]] [[nontrivial APS|nontrivial]] [[saturated sub-APS|saturated]] [[sub-IAPS]]. Equivalently, it is a simple object in the category of IAPSes with IAPS homomorphisms. |
==Definition== | ==Definition== | ||
Current revision as of 23:45, 25 January 2007
Contents |
[edit] Definition
[edit] Symbol-free definition
An IAPS of groups is termed i-simple if it has no proper nontrivial saturated sub-IAPS. Equivalently, it is a simple object in the category of IAPSes with IAPS homomorphisms.
[edit] Definition
[edit] 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.
