2-torsion-free group of nilpotency class two
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: 2-torsion-free group and group of nilpotency class two
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Definition
A group is termed a 2-torsion-free group of nilpotency class two if it is both a 2-torsion-free group and a group of nilpotency class two, i.e., its nilpotency class is at most two.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Baer Lie group | 2-powered group of nilpotency class two | |FULL LIST, MORE INFO | ||
| UCS-Baer Lie group | group of nilpotency class two whose center is 2-powered | |FULL LIST, MORE INFO | ||
| LUCS-Baer Lie group | group of nilpotency class two where every element of the derived subgroup has a unique square root | |FULL LIST, MORE INFO |