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