The Structure of F-Quasigroups
Group Theory
2008-01-15 v2
Abstract
We solve a problem of Belousov which has been open since 1967: to characterize the loop isotopes of F-quasigroups. We show that every F-quasigroup has a Moufang loop isotope which is a central product of its nucleus and Moufang center. We then use the loop to reveal the structure of the associated F-quasigroup.
Cite
@article{arxiv.math/0510298,
title = {The Structure of F-Quasigroups},
author = {Tomáš Kepka and Michael K. Kinyon and J. D. Phillips},
journal= {arXiv preprint arXiv:math/0510298},
year = {2008}
}
Comments
24 pages. v.2 incorporates minor changes suggested by the referee. To appear in the Journal of Algebra