The Structure of F-Quasigroups
arXiv:math/0510298
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.
24 pages. v.2 incorporates minor changes suggested by the referee. To appear in the Journal of Algebra