Baer diassociative loop
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A Baer diassociative loop is a diassociative loop satisfying the following two conditions:
- 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)
- The loop is uniquely 2-divisible, i.e., for every , there is a unique such that .