Bounded-nilpotent IAPS: Difference between revisions
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{{analogue of property| | |||
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==Definition== | ==Definition== | ||
A ''bounded-nilpotent IAPS''' is an [[IAPS of groups]] such that the following equivalent conditions are satisfied: | 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 | * The [[lower central sub-IAPS series]] terminates, in finitely many steps, at the trivial sub-IAPS | ||
Latest revision as of 20:08, 24 August 2008
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