# Bounded-nilpotent IAPS

From Groupprops

This term is related to: APS theory

View other terms related to APS theory | View facts related to APS theory

*This article defines a property that can be evaluated for an IAPS of groups*

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

ANALOGY: This is an analogue in IAPS of a property encountered in group. Specifically, it is a IAPS property analogous to the group property: nilpotent group

View other analogues of nilpotent group | View other analogues in IAPSs of group properties (OR, View as a tabulated list)

## 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