Results 81 to 90 of about 136 (119)

Isotopy of abelian quasigroups [PDF]

Proceedings of the American Mathematical Society, 1977
It is proved that every abelian quasigroup possesses a class of isomorphic principal isotopes which are commutative groups. Also it is indicated how the corresponding result for topological quasigroups can be utilised to obtain results for abelian topological quasigroups from analogous results for commutative topological groups.
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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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Certain congruences on quasigroups [PDF]

Proceedings of the American Mathematical Society, 1952
1. Using the ideas of [1],1 we define a lattice-isomorphism between the reversible congruences on a quasigroup and certain congruences on its group of translations. This may be used to get certain properties of the quasigroup congruences from those of the translation-group congruences; for example, it gives a new proof that reversible congruences on a ...
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Sharp Characters of Quasigroups

European Journal of Combinatorics, 1993
The idea of a sharp permutation character of a group arises from combinatorial considerations. Recent work, founded on early results of H. F. Blichfeldt published in 1904, has shown that the definition of sharpness can be extended to arbitrary group characters, and in fact it has emerged that the natural object to define is a sharp triple.
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Sub-quasigroups of finite quasigroups [PDF]

Pacific Journal of Mathematics, 1957
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Parastrophes of quasigroups

, 2015
Parastrophes (conjugates) of a quasigroup can be divided into separate classes containing isotopic parastrophes. We prove that the number of such classes is always 1, 2, 3 or 6. Next we characterize quasigroups having a fixed number of such classes.
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Graph decomposition and quasigroup identities

Le Matematiche, 1990
See directly the article.
Curt Lindner
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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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An algorithm for judging and generating multivariate quadratic quasigroups over Galois fields. [PDF]

Springerplus, 2016
Zhang Y, Zhang H.
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Abelian quasigroups and T-quasigroups

, 1994
By means of known results with respect to algebras of a congruence modular variety it is proved that abelian in the sense of McKenzie quasigroups, i.e. quasigroups coinciding with their centre, are T-quasigroups and conversely.
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