3-locally nilpotent group
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 is termed a 3-locally nilpotent group if, for any subset of size at most three in the group, the subgroup generated by the subset is a nilpotent group.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| abelian group | |FULL LIST, MORE INFO | |||
| group of nilpotency class two | |FULL LIST, MORE INFO | |||
| nilpotent group | |FULL LIST, MORE INFO | |||
| locally nilpotent group | |FULL LIST, MORE INFO | |||
| Lazard Lie group | |FULL LIST, MORE INFO | |||
| LCS-Lazard Lie group | |FULL LIST, MORE INFO |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| 2-locally nilpotent group | |FULL LIST, MORE INFO |