Group of nilpotency class two whose derived subgroup is 2-divisible

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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 G is termed a group of nilpotency class two whose derived subgroup is 2-divisible if it satisfies both the following conditions:

  1. G is a group of nilpotency class two.
  2. The derived subgroup G' is a 2-divisible group, i.e., every element of the derived subgroup has a square root in the derived subgroup.

Relation with other properties

Stronger properties

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

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
group of nilpotency class two whose derived subgroup is in the square of its center |FULL LIST, MORE INFO