The varieties of loops of Bol-Moufang type

Simple item page
dc.creatorPhillips, J. D.
dc.creatorVojtěchovský, Petr
dc.date2007-01-24
dc.date.accessioned2026-07-07T07:42:53Z
dc.date.available2026-07-07T07:42:53Z
dc.descriptionA 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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0701714
dc.identifierhttp://arxiv.org/abs/math/0701714
dc.identifierAlgebra Universalis 54 (2005), no. 3, 259-271
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122614
dc.subjectGroup Theory
dc.subject20N05
dc.titleThe varieties of loops of Bol-Moufang type
dc.typetext

Files

Collections

arXiv