Baer diassociative loop

Definition
A Baer diassociative loop is a diassociative loop $$L$$ satisfying the following two conditions:


 * 1) The subgroup generated by any two elements is a group of nilpotency class two (note that diassociativit per se simply says that any two elements generate a subgroup)
 * 2) The loop is uniquely 2-divisible, i.e., for every $$a \in L$$, there is a unique $$b \in L$$ such that $$b^2 = a$$.