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Displaying similar documents to “Multiplication groups of free loops. I”

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 ) ) .

Lexicographic product decompositions of half linearly ordered loops

Milan Demko (2007)

Czechoslovak Mathematical Journal

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In this paper we prove for an hl-loop Q an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop Q with a finite number of lexicographic factors have isomorphic refinements.