On quasiidentities of transitive quasigroups
Ján Duplák (1984)
Mathematica Slovaca
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Ján Duplák (1984)
Mathematica Slovaca
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V. A. Shcherbacov, D. I. Pushkashu (2010)
Commentationes Mathematicae Universitatis Carolinae
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Information on the structure of finite paramedial quasigroups, including a classification of finite simple paramedial quasigroups, is given. The problem ``Classify the finite simple paramedial quasigroups'' was posed by J. Ježek and T. Kepka at the conference LOOPS'03, Prague 2003.
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...
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...