Baer diassociative loop

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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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.