Baer Moufang loop

Definition
A Baer Moufang loop is a Moufang loop $$M$$ satisfying the following two conditions:


 * 1) The subloop generated by any two elements, which must be a subgroup, is a group of nilpotency class two.
 * 2) The loop is uniquely 2-divisible, i.e., for every $$a \in M$$, there is a unique $$b \in M$$ such that $$b^2 = a$$.

Stronger properties

 * Weaker than::Baer Lie group

Weaker properties

 * Stronger than::Baer diassociative loop