Baer Moufang loop

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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.

Relation with other properties

Stronger properties

Weaker properties