Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture.

Pula, Kyle

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Displaying similar documents to “Products of all elements in a loop and a framework for non-associative analogues of the Hall-Paige conjecture.”

Groups, transversals, and loops

Tuval Foguel (2000)

Commentationes Mathematicae Universitatis Carolinae

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A family of loops is studied, which arises with its binary operation in a natural way from some transversals possessing a ``normality condition''.

Identities and the group of isostrophisms

Aleš Drápal, Viktor Alekseevich Shcherbakov (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we reexamine the concept of isostrophy. We connect it to the notion of term equivalence, and describe the action of dihedral groups that are associated with loops by means of isostrophy. We also use it to prove and present in a new way some well known facts on $m$ -inverse loops and middle Bol loops.

Commutative subloop-free loops

Martin Beaudry, Louis Marchand (2011)

Commentationes Mathematicae Universitatis Carolinae

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We describe, in a constructive way, a family of commutative loops of odd order, $n \geq 7$ , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group $𝒜_{n}$ .

Schreier loops

Péter T. Nagy, Karl Strambach (2008)

Czechoslovak Mathematical Journal

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We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.