Displaying similar documents to “Bicrossproduct Hopf quasigroups”

On B * -quasigroups.

Beg, Afzal (1998)

Bulletin of the Malaysian Mathematical Society. Second Series

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A geometric approach to universal quasigroup identities

Václav J. Havel (1993)

Archivum Mathematicum

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In the present paper we construct the accompanying identity I ^ of a given quasigroup identity I . After that we deduce the main result: I is isotopically invariant (i.e., for every guasigroup Q it holds that if I is satisfied in Q then I is satisfied in every quasigroup isotopic to Q ) if and only if it is equivalent to I ^ (i.e., for every quasigroup Q it holds that in Q either I , I ^ are both satisfied or both not).

F-quasigroups isotopic to groups

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...