On -quasigroups.
Beg, Afzal (1998)
Bulletin of the Malaysian Mathematical Society. Second Series
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Beg, Afzal (1998)
Bulletin of the Malaysian Mathematical Society. Second Series
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Ján Duplák (1984)
Mathematica Slovaca
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Tomáš Kepka, Michael K. Kinyon, Jon D. Phillips (2010)
Commentationes Mathematicae Universitatis Carolinae
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In Kepka T., Kinyon M.K., Phillips J.D., , , we showed that every loop isotopic to an F-quasigroup is a Moufang loop. Here we characterize, via two simple identities, the class of F-quasigroups which are isotopic to groups. We call these quasigroups FG-quasigroups. We show that FG-quasigroups are linear over groups. We then use this fact to describe their structure. This gives us, for instance, a complete description of the simple FG-quasigroups. Finally, we show an equivalence of equational...
Ján Duplák (1988)
Czechoslovak Mathematical Journal
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Alimpic, Branka P. (1981)
Publications de l'Institut Mathématique. Nouvelle Série
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Fedir M. Sokhatsky, Halyna V. Krainichuk (2012)
Commentationes Mathematicae Universitatis Carolinae
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We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like...