2010/05/16 by J. D. Phillips, Phillips, J. D., V. A. Shcherbacov +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1005.2750
6 pages
arxiv created 2010/05/16 · arxiv updated 2010/05/18
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.