Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

Cheban loops


J.D.Phillips a and V.A.Shcherbacov

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 by A. M. Cheban. 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.


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