Results 81 to 90 of about 1,878 (148)
, 2011 The article is devoted to linear quasigroups and some of their generalizations. In the first part main definitions and notions of the theory of quasigroups are given. In the second part some elementary properties of linear quasigroups and their generalizations are presented.
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Investigation of Some Cryptographic Properties of the 8x8 S-boxes Created by Quasigroups [PDF]
Computer Science Journal of Moldova, 2020 We investigate several cryptographic properties in 8-bit S-boxes obtained by quasigroups of order 4 and 16 with several different algebraic constructions.
Aleksandra Mileva +3 more
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On free quasigroups and quasigroup representations
, 2018 This work consists of three parts. The discussion begins with \emph{linear quasigroups}. For a unital ring $S$, an $S$-linear quasigroup is a unital $S$-module, with automorphisms $\rho$ and $\lambda$ giving a (nonassociative) multiplication $x\cdot y=x^\rho+y^\lambda$. If $S$ is the field of complex numbers, then ordinary characters provide a complete
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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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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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Generation of Multivariate Quadratic Quasigroups by Proper Families of Boolean Functions
Journal of Mathematical Sciences, 2022 A. V. Galatenko, V. Nosov, A. Pankratiev
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Sub-quasigroups of finite quasigroups [PDF]
Pacific Journal of Mathematics, 1957 openaire +2 more sources
, 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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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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