Results 101 to 110 of about 3,309 (193)
On Multiplication Groups of Quasigroups
European Journal of Combinatorics, 1984 The author shows that all finite dihedral, symmetric, alternating, general linear and projective general linear groups and the Mathieu- groups \(M_{11}\) and \(M_{23}\) have the following property: they are isomorphic to multiplication groups of quasigroups.
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, 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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Branched covers induced by semisymmetric quasigroup homomorphisms [PDF]
, 2023 Kyle Lewis
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A Note on Trimedial Quasigroups
, 2002 2 pages, AMS-LaTeX, submitted to_Quasigroups and Related ...
Kinyon, M.K., Phillips, J.
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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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On the Constant-Depth Circuit Complexity of Generating Quasigroups [PDF]
TheoretiCSWe investigate the constant-depth circuit complexity of the Isomorphism Problem, Minimum Generating Set Problem (MGS), and Sub(quasi)group Membership Problem (Membership) for groups and quasigroups (=Latin squares), given as input in terms of their ...
Nathaniel A. Collins +3 more
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Quasigroups, right quasigroups, coverings and representations
, 2018 For a fixed quasigroup Q, equivalences are established between the following categories: (i) the category of modules over the quasigroup; (ii) the category of representations of a stabilizer in the universal multiplication group; (iii) the category of representations of the fundamental groupoid of the Cayley diagram of the quasigroup in the category of
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On Birkhoff's quasigroup axioms
Journal of Algebra, 2016 Quasigroups form a variety only if two additional operations, namely \(/\) and \(\backslash\) are considered. Birkhoff formulated six identities that define equationally the variety of quasigroups. Evans proved that only the most natural four identities are needed.
Phillips, J. D. +3 more
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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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