Cheban loops

J. D. Phillips; V. A. Shcherbacov

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arXiv · 1005.2750

Cheban loops

J. D. Phillips·V. A. Shcherbacov

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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 in Cheban, A. M. Loops with identities of length four and of rank three. II. (Russian) General algebra and discrete geometry, pp. 117-120, 164, "Shtiintsa", Kishinev, 1980. 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. 2010-05-16. Cheban loops. https://arxiv.org/abs/1005.2750

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