Cheban loops
Group Theory
2010-05-18 v1
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.
Cite
@article{arxiv.1005.2750,
title = {Cheban loops},
author = {J. D. Phillips and V. A. Shcherbacov},
journal= {arXiv preprint arXiv:1005.2750},
year = {2010}
}
Comments
6 pages