Global LCS-Lazard Lie 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 global LCS-Lazard Lie group if it satisfies the following two conditions:

1. It is a nilpotent group.
2. Its lower central series powering threshold is $\infty$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
global Lazard Lie group				|FULL LIST, MORE INFO
LCS-Baer Lie group	group of nilpotency class two where the derived subgroup is 2-powered			|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
LCS-Lazard Lie group				|FULL LIST, MORE INFO