Open Access
2010 Cheban loops
J. D. Phillips, V. A. Shcherbacov
J. Gen. Lie Theory Appl. 4: 1-5 (2010). DOI: 10.4303/jglta/G100501


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.


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J. D. Phillips. V. A. Shcherbacov. "Cheban loops." J. Gen. Lie Theory Appl. 4 1 - 5, 2010.


Published: 2010
First available in Project Euclid: 11 October 2011

zbMATH: 1197.20059
MathSciNet: MR2719414
Digital Object Identifier: 10.4303/jglta/G100501

Primary: 20N05

Rights: Copyright © 2010 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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