The Structure of F-Quasigroups

J. D. Phillips; Michael K. Kinyon; Tom\'a\v{s} Kepka

arxiv: math/0510298 · v2 · submitted 2005-10-14 · 🧮 math.GR

The Structure of F-Quasigroups

Tom\'a\v{s} Kepka , Michael K. Kinyon , J. D. Phillips This is my paper

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keywords loopf-quasigroupf-quasigroupsmoufangstructureassociatedbeenbelousov

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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.

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The Structure of F-Quasigroups

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