alexa Cheban loops
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Cheban loops

J. D. Phillips1 and V. A. Shcherbacov 2

1Department of Mathematics and Computer Science, Northern Michigan University, Marquette, MI 49855, USA

2Institute of Mathematics, Academy of Sciences of Moldova, str. Academiai 5, MD 2028, Chisinau, Moldova E-mails: [email protected], [email protected]

Received Date: February 1, 2010; Revised Date: April 11, 2010

 

Abstract

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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