Bounded-nilpotent IAPS

This term is related to: APS theory
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This article defines a property that can be evaluated for an IAPS of groups

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ANALOGY: This is an analogue in IAPSs of the group property:
View other analogues of nilpotent group | View other analogues in IAPSs of group properties

Definition

A bounded-nilpotent IAPS is an IAPS of groups such that the following equivalent conditions are satisfied:

• The lower central sub-IAPS series terminates, in finitely many steps, at the trivial sub-IAPS
• Every member is a nilpotent group and there is a common finite bound on the nilpotence class of all members

Relation with other properties

Stronger properties

• Abelian IAPS

Weaker properties

• Bounded-solvable IAPS
• Nilpotent IAPS
• Solvable IAPS