# Lazard Lie property is not subgroup-closed

From Groupprops

This article gives the statement, and possibly proof, of a group property (i.e., Lazard Lie group)notsatisfying a group metaproperty (i.e., subgroup-closed group property).

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## Statement

It is possible to have a Lazard Lie group and a subgroup of that is *not* a Lazard Lie group.

## Related facts

### Similar facts

### Opposite facts

## Proof

`Further information: unitriangular matrix group:UT(3,Q), unitriangular matrix group:UT(3,Z)`

Consider the example and . is a Lazard Lie group (in fact, a Baer Lie group). is a group of class exactly two that is not 2-powered, hence, it is not a Lazard Lie group.