# Baer Lie group

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## Contents

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This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: group of nilpotency class and uniquely 2-divisible group
View other group property conjunctions OR view all group properties

## Definition

A Baer Lie group is a group $G$ satisfying the following two conditions:

1. It is a nilpotent group of class two, i.e., its nilpotency class is at most two.
2. It is a uniquely 2-divisible group: For every $g \in G$, there is a unique element $h \in G$ such that $h^2 = g$.

A Baer Lie group is a group that can serve on the group side of a Baer correspondence, i.e., it has a corresponding Baer Lie ring.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
odd-order abelian group
class two p-group for odd prime $p$

### Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Lazard Lie group