Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Cheban loops

Abstract

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.