Journal Title/Source
Algebra Universalis
Publication Date
2005
Volume
54
Page Numbers
259–271
Document Type
Journal Article
Department
Mathematics and Computer Science
Abstract
A loop identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, and the order in which the variables appear on both sides is the same, viz. ((xy)x)z = x(y(xz)). Loop varieties defined by one identity of Bol-Moufang type include groups, Bol loops, Moufang loops and C-loops. We show that there are exactly 14 such varieties, and determine all inclusions between them, providing all necessary counterexamples, too. This extends and completes the programme of Fenyves [5].
Recommended Citation
Phillips, J.D., "The Varieties of Loops of Bol-Moufang Type" (2005). Journal Articles. 534.
https://commons.nmu.edu/facwork_journalarticles/534