Group of nilpotency class three
From Groupprops
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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Contents
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 |
