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Displaying similar documents to “Quadratic level quasigroup equations with four variables. I.”

Axioms for trimedial quasigroups

Michael K. Kinyon, Jon D. Phillips (2004)

Commentationes Mathematicae Universitatis Carolinae

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We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are trimedial.

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.