# Baer Lie group

From Groupprops

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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 satisfying the following two conditions:

- It is a nilpotent group of class two, i.e., its nilpotency class is at most two.
- It is a uniquely 2-divisible group: For every , there is a unique element such that .

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 |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Lazard Lie group |