Displaying similar documents to “Corrigendum to “Realizations of Loops and Groups defined by short identities””

Realizations of Loops and Groups defined by short identities

Anthony Donald Keedwell (2009)

Commentationes Mathematicae Universitatis Carolinae

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In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results.

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...

A short direct characterization of GS-quasigroups

Zdenka Kolar-Begović (2011)

Czechoslovak Mathematical Journal

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The theorem about the characterization of a GS-quasigroup by means of a commutative group in which there is an automorphism which satisfies certain conditions, is proved directly.

On B * -quasigroups.

Beg, Afzal (1998)

Bulletin of the Malaysian Mathematical Society. Second Series

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On quasigroups with the left loop property

A. Nourou Issa (2000)

Commentationes Mathematicae Universitatis Carolinae

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Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.