A Moufang loop is a loop Q that satisfies the following equivalent identities (the binary operation in Q is denoted by juxtaposition):
- z(x(zy)) = ((zx)z)y
- x(z(yz)) = ((xz)y)z
- (zx)(yz) = (z(xy))z
- (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