Lazard Lie property is not subgroup-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., subgroup-closed group property).
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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.