Results 101 to 110 of about 2,017 (174)

Isotopy and parastrophy of quasigroups [PDF]

Proceedings of the American Mathematical Society, 1963
1. It has been noted that every quasigroup (Q, *) belongs to a set of 6 quasigroups, called adjugate by Fisher and Yates [4], conjugate by Stein [6], parastrophic by Sade [5]. If in (Q, *), xy=z, then in the parastrophic quasigroups (xx) (x) (yx) = zw, where wr is one of the 6 permutations of {x, yy,Z }, v7r the image of vI{xI y, Z } under wx, and (wx)
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Varieties of Hexagonal Quasigroups

Journal of Algebra, 1993
The decomposition of a complete graph into disjoint cycles can be used to define a binary operation \(\star\) on the vertices of the graph -- if a cycle is \((\dots, a, b, c, \dots)\) then \(a \star b = c\) and \(c \star b = a\). In general the groupoid thus obtained is not a quasigroup, but when the decomposition satisfies an extra condition, known as
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On a quasigroup prolongation and its recursive differentiability

Acta et Commentationes: Ştiinţe Exacte şi ale Naturii
We consider a method of quasigroups prolongation by adding two new elements and by using two transversals that intersect in exactly one cell. In a Latin square L of order q, along with usual transversals we call "free transversals" any set of q cells ...
Elena Cuznețov
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SAC loops and loops of order five

Математика, інформатика, фізика: наука та освіта
In this article, we continue the analytical research of small-order loops. Namely, we investigate loops of order 5. Recall that an element of a loop is called unipotent if its square is neutral.
Fedir Sokhatsky
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A Note on the Quasigroup of Lai–Massey Structures

Cryptography
In our paper, we explore the consequences of replacing the commutative group operation used in Lai–Massey structures with a quasigroup operation. We introduce four quasigroup versions of the Lai–Massey structure and prove that for quasigroups isotopic ...
George Teşeleanu
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Sub-quasigroups of finite quasigroups [PDF]

Pacific Journal of Mathematics, 1957
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Graph decomposition and quasigroup identities

Le Matematiche, 1990
See directly the article.
Curt Lindner
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Parastrophic-orthogonal ternary medial quasigroups with 3 and 4 distinct parastrophes

Математика, інформатика, фізика: наука та освіта
In the article, we study parastrophic-orthogonal ternary quasigroups: namely, group isotopes which have 3 and 4 distinct parastrophes. The necessary and sufficient conditions for ternary medial quasigroups with 3 and 4 distinct parastrophes to be ...
Iryna Fryz, Yevhen Pirus
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Parallelograms in quadratical quasigroups

Quasigroups and related systems, 2010
The "geometric" concept of parallelogram is introduced and investigated in a general quadratical quasigroup and geometrical interpretation in a quadratical quasigroup $C(1/2(1+i)))$ is given. Some statements about relationships between the parallelograms and some other geometric structures in a general quadratical quasigroup will be also considered.
Volenec, Vladimir, Kolar-Šuper, Ružica
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Symmetries in hexagonal quasigroups [PDF]

Archivum Mathematicum, 2007
Hexagonal quasigroup is idempotent medial and semisymmetric quasigroup. In this article we define and study symmetries about a point, segment and ordered triple of points in hexagonal quasigroups. The main results are the theorems on composition of two and three symmetries.
Volenec, Vladimir, Bombardelli, Mea
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