Baer diassociative loop

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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 $b^{2}=a$.