Nilpotent loop

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This article defines a property that can be evaluated for a loop.
View other properties of loops
ANALOGY: This is an analogue in loop of a property encountered in group. Specifically, it is a loop property analogous to the group property: nilpotent group
View other analogues of nilpotent group | View other analogues in loops of group properties (OR, View as a tabulated list)

Definition

A nilpotent loop (also called a centrally nilpotent loop) is a loop whose upper central series reaches the whole loop in finitely many steps.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
nilpotent Moufang loop
nilpotent group

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
solvable loop