3-locally nilpotent group

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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 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 Locally 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 2-locally nilpotent group|FULL LIST, MORE INFO