Displaying similar documents to “Ternary quasigroups and the modular group”

m -medial n -quasigroups

Tomáš Kepka (1991)

Commentationes Mathematicae Universitatis Carolinae

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For n ≥ 4 , every n -medial n -quasigroup is medial. If 1 ≤ m < n , then there exist m -medial n -quasigroups which are not ( m + 1 ) -medial.

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).

Invertibility criterion of composition of two multiary quasigroups

Fedir M. Sokhatsky, Iryna V. Fryz (2012)

Commentationes Mathematicae Universitatis Carolinae

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We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for T -quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and n -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We...