  Left Cheban loops are loops that satisfy the identity x(xy.z) = yx.xz. Right
Cheban loops satisfy the mirror identity {(z.yx)x = zx.xy}. Loops that are both
left and right Cheban are called Cheban loops. Cheban loops can also be
characterized as those loops that satisfy the identity x(xy.z) = (y.zx)x. These
loops were introduced in Cheban, A. M. Loops with identities of length four and
of rank three. II. (Russian) General algebra and discrete geometry, pp.
117-120, 164, "Shtiintsa", Kishinev, 1980. Here we initiate a study of their
structural properties. Left Cheban loops are left conjugacy closed. Cheban
loops are weak inverse property, power associative, conjugacy closed loops;
they are centrally nilpotent of class at most two.
