Baer Lie property is not quotient-closed

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This article gives the statement, and possibly proof, of a group property (i.e., Baer Lie group) not satisfying a group metaproperty (i.e., quotient-closed group property).
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Statement

It is possible to have a Baer Lie group G and H a normal subgroup of G such that the quotient group G/H is not a Baer Lie group.

Related facts

Proof

Further information: unitriangular matrix group:UT(3,Q), quotient of UT(3,Q) by a central Z

Suppose G is the group UT(3,\mathbb{Q}), the unitriangular matrix group of degree three over the field of rational numbers. Let H be a central subgroup of G that is isomorphic to \mathbb{Z}, the group of integers. The quotient group G/H = UT(3,\mathbb{Q})/\mathbb{Z} is not a Baer Lie group: it is a group of nilpotency class exactly two that has 2-torsion.