Baer Lie group

Definition
A Baer Lie group is a group $$G$$ satisfying the following two conditions:


 * 1) It is a defining ingredient::nilpotent group of class two, i.e., its defining ingredient::nilpotency class is at most two.
 * 2) It is a defining ingredient::2-powered group: For every $$g \in G$$, there is a unique element $$h \in G$$ such that $$h^2 = g$$.

Given condition (1), condition (2) is equivalent to requiring that $$G$$ be both 2-torsion-free (i.e., no element of order two) and 2-divisible. (see equivalence of definitions of nilpotent group that is torsion-free for a set of primes).

A Baer Lie group is a group that can serve on the group side of a Baer correspondence, i.e., it has a corresponding Baer Lie ring.