Moufang Loop

A Moufang loop is a loop Q that satisfies the following equivalent identities (the binary operation in Q is denoted by juxtaposition):

  1. z(x(zy)) = ((zx)z)y
  2. x(z(yz)) = ((xz)y)z
  3. (zx)(yz) = (z(xy))z
  4. (zx)(yz) = z((xy)z)

for all x, y, z in Q. These identities are known as Moufang identities.

Read more about Moufang Loop:  Examples, Open Problems