Group of nilpotency class three

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group of nilpotency class three is defined as a nilpotent group whose nilpotency class is at most three.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
abelian group
group of nilpotency class two

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group of 3-local nilpotency class three
group of Levi class two
3-Engel group
nilpotent group