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Quadratic Level Quasigroup Equations With Four Variables II: the Lattice of Varieties

Aleksandar Krapež (2013)

Publications de l'Institut Mathématique

Quantum idempotence, distributivity, and the Yang-Baxter equation

J. D. H. Smith (2016)

Commentationes Mathematicae Universitatis Carolinae

Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.

Quasigroup automorphisms and symmetric group characters

Brent Kerby, Jonathan D. H. Smith (2010)

Commentationes Mathematicae Universitatis Carolinae

The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a $λ$ -ideal of the special $λ$ -ring of symmetric group class functions.

Quasigroup covers of division groupoids

Jaroslav J. Ježek, Tomáš Kepka, Petr Němec (2023)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a division groupoid that is not a quasigroup. For each regular cardinal $α > | G |$ we construct a quasigroup $Q$ on $G \times α$ that is a quasigroup cover of $G$ (i.e., $G$ is a homomorphic image of $Q$ and $G$ is not an image of any quasigroup that is a proper factor of $Q$ ). We also show how to easily obtain quasigroup covers from free quasigroups.

Quasigroups and Factorisation of Complete Digraphs

Bohdan Zelinka (1973)

Matematický časopis

Quasigroups and tactical systems.

Ronald D. Baker (1978)

Aequationes mathematicae

Quasigroups arisen by right nuclear extension

Péter T. Nagy, Izabella Stuhl (2012)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to prove that a quasigroup $Q$ with right unit is isomorphic to an $f$ -extension of a right nuclear normal subgroup $G$ by the factor quasigroup $Q / G$ if and only if there exists a normalized left transversal $Σ \subset Q$ to $G$ in $Q$ such that the right translations by elements of $Σ$ commute with all right translations by elements of the subgroup $G$ . Moreover, a loop $Q$ is isomorphic to an $f$ -extension of a right nuclear normal subgroup $G$ by a loop if and only if $G$ is middle-nuclear, and there exists...