Displaying similar documents to “On median point of the system of elements of A -structure”

Affine regular decagons in GS-quasigroup

Vladimír Volenec, Zdenka Kolar-Begović (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup ℂ ( 1 2 ( 1 + 5 ) ) .

Medial quasigroups of type ( n , k )

Alena Vanžurová (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Our aim is to demonstrate how the apparatus of groupoid terms (on two variables) might be employed for studying properties of parallelism in the so called ( n , k ) -quasigroups. We show that an incidence structure associated with a medial quasigroup of type ( n , k ) , n > k ≥ 3 , is either an affine space of dimension at least three, or a desarguesian plane. Conversely, if we start either with an affine space of order k > 2 and dimension m , or with a desarguesian affine plane of order k > 2 then there is a medial quasigroup...