2-torsion-free group of nilpotency class two

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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