The Structure of F-Quasigroups

Details The Structure of F-Quasigroups The Structure of F-Quasigroups

2005-10-14

arxiv.org/abs/math/0510298v2

J. Algebra 317 (2007), 435-461

Mathematics

Group Theory

24 pages. v.2 incorporates minor changes suggested by the referee. To appear in the Journal of Algebra

Scientific paper

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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