Global LUCS-Lazard Lie group
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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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A group is termed a global LUCS-Lazard Lie group if there exists a positive integer such that:
- is a nilpotent group of nilpotency class at most .
- The following equivalent formulations:
- For every positive integer , every element of the lower central series member has a unique root in for all .
- For every positive integer , every element of the lower central series member has a unique root in the upper central series member for all .
- For every positive integer , every element of the lower central series member has unique roots in for all , and this root is inside .
Equivalence of definitions
Further information: equivalence of definitions of global LUCS-Lazard Lie group
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|LUCS-Baer Lie group|||FULL LIST, MORE INFO|
|global Lazard Lie group|||FULL LIST, MORE INFO|