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Showing 1 to 10 of 10 for “"Quasigroups"”.
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On Multiplication Groups of Quasigroups
<p>Quasigroups are algebraic structures in which divisibility is always defined. In this thesis we investigate quasigroups using a group-theoretic approach. We first construct a family of quasigroups which behave in a group-like fashion. We then focus on the multiplication groups of quasigroups, …
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Algebraic Structures and Variations: From Latin Squares to Lie Quasigroups
… operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a …
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QUOTIENTS, EQUIVALENCE RELATIONS, AND NORMALITY IN NON-ASSOCIATIVE ALGEBRA WITH REGARDS TO LOOPS AND QUASIGROUPS
… of relations, quotients, normality, loops, quasigroups, and related theorems and varieties. Nonassociative algebra is a relatively new area of mathematics, it came about in the past hundred years, and has started making progress in the past 60 years. In nonassociative algebra, varieties do …
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On Loop Commutators, Quaternionic Automorphic Loops, and Related Topics
… groups.</p> <p>Lastly, we find varieties of quasigroups which are isotopic to commutative Moufang loops and prove their full characterization. Moreover, we define a new variety of quasigroups motivated by the semimedial quasigroups and show that they have an affine representation over …
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Topics in Moufang Loops
… groups. We proceed to investigate para-F quasigroups, a variety of quasigroups which we show are antilinear over Moufang loops. We briefly depart from the context of Moufang loops to discuss solvability in general loops. We then prove some results on the cosets of subloops of Moufang …
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Dynamic key scheduling algorithm for block ciphers using quasigroup string transformation
… “Isotophism”, which literally means Different quasigroups that has the same order of elements but different arrangements can be generated from the existing one. This research proposed a Dynamic Key Scheduling Algorithm (KSA) using isotope of a quasigroup as the dynamic substitution table. A …
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Tópicos de planeamento de experiências : uma abordagem estatística, computacional e matemática
… provide with the orthogonally concept, and the Quasigroups theory, the Incidence Plan’s and also the Graphs. It will also be investigated and illustrated some specificities of application of some types of design in ludic and recreational areas such as Sudoku, Skyscrapers Puzzle, and the Latin …
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Games on graphs, visibility representations, and graph colorings
… of A-cordiality involving digraphs and quasigroups, and we show that there are infinitely many Q-cordial digraphs for every quasigroup Q."
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Finite model enumeration
… (groups, semigroups, and their ordered versions, quasigroups, fields, rings, MV-algebras, lattices, etc.), mathematicians resort to libraries of all models, up to isomorphism, of order n (for small values of n) of the classes of algebras they are interested in. These libraries allow …