Journal of Generalized Lie Theory and Applications

Cheban loops

J. D. Phillips and V. A. Shcherbacov

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Left Cheban loops are loops that satisfy the identity $x(xy \cdot z) = yx \cdot xz$. Right Cheban loops satisfy the mirror identity $(z \cdot yx)x = zx \cdot xy$. 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 $x(xy \cdot z) = (y \cdot zx)x$. 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.

Article information

J. Gen. Lie Theory Appl., Volume 4 (2010), Article ID G100501, 5 pages.

First available in Project Euclid: 11 October 2011

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Zentralblatt MATH identifier

Primary: 20N05: Loops, quasigroups [See also 05Bxx]


Phillips, J. D.; Shcherbacov, V. A. Cheban loops. J. Gen. Lie Theory Appl. 4 (2010), Article ID G100501, 5 pages. doi:10.4303/jglta/G100501.

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