LCS-Baer Lie group

Direct definition
A LCS-Baer Lie group or lower central series Baer Lie group is a group satisfying both the following properties:


 * 1) It is a defining ingredient::group of nilpotency class two, i.e., its nilpotency class is at most two.
 * 2) Its derived subgroup is a uniquely 2-divisible group. Note that since the group has class at most two, the derived subgroup must also be abelian.

Definition in terms of LCS-Lazard Lie group
A LCS-Baer Lie group is a LCS-Lazard Lie group that is also a group of nilpotency class two.