Lazard Lie property is not finite direct product-closed
This article gives the statement, and possibly proof, of a group property (i.e., Lazard Lie group) not satisfying a group metaproperty (i.e., finite direct product-closed group property).
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Take to be a Baer Lie group that is not abelian, for instance, for some odd prime number . Take to be a nontrivial abelian 2-group. Note that is a class two Lazard Lie group and is a class one Lazard Lie group. The external direct product is not a Lazard Lie group.