Schreier loops
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.
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Péter T. Nagy, Karl Strambach (2008)
Czechoslovak Mathematical Journal
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.
Markovski, S., Gligoroski, D., Stojčevska, B. (2000)
Novi Sad Journal of Mathematics
Jaroslav Ježek, Tomáš Kepka (1997)
Czechoslovak Mathematical Journal
After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.
Tomáš Kepka, Petr Němec (2003)
Acta Universitatis Carolinae. Mathematica et Physica
Jaroslav Ježek, Tomáš Kepka (2006)
Acta Universitatis Carolinae. Mathematica et Physica
David Stanovský (2011)
Acta Universitatis Carolinae. Mathematica et Physica
Baumeister, Barbara, Stein, Alexander (2010)
Beiträge zur Algebra und Geometrie
Zoran Stojakovic, Djura Paunic (1986)
Aequationes mathematicae
Zoran Stojakovic, Djura Paunic (1985)
Aequationes mathematicae
Jaroslav Ježek, Tomáš Kepka (1981)
Commentationes Mathematicae Universitatis Carolinae
Renato Migliorato (1986)
Annales scientifiques de l'Université de Clermont. Mathématiques
Jonathan D. H. Smith (2020)
Commentationes Mathematicae Universitatis Carolinae
The semisymmetrization of an arbitrary quasigroup builds a semisymmetric quasigroup structure on the cube of the underlying set of the quasigroup. It serves to reduce homotopies to homomorphisms. An alternative semisymmetrization on the square of the underlying set was recently introduced by A. Krapež and Z. Petrić. Their construction in fact yields a Mendelsohn quasigroup, which is idempotent as well as semisymmetric. We describe it as the Mendelsohnization of the original quasigroup. For quasigroups...
Dwight Steedley (1974)
Aequationes mathematicae
Cristea, Irina (2009)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Tomáš Kepka, Petr Němec (1996)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Jung R. Cho, Jaroslav Ježek, Tomáš Kepka (1999)
Czechoslovak Mathematical Journal
Tomáš Kepka, K. K. Ščukin (1993)
Commentationes Mathematicae Universitatis Carolinae
Simple quasigroups with commuting inner permutations are medial.
Robert El Bashir, Jaroslav Ježek, Tomáš Kepka (2000)
Czechoslovak Mathematical Journal
This short note is a continuation of and and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of .
Václav Havel, Josef Klouda (1993)
Commentationes Mathematicae Universitatis Carolinae
Under a multigraph it is meant in this paper a general incidence structure with finitely many points and blocks such that there are at least two blocks through any point and also at least two points on any block. Using submultigraphs with saturated points there are defined generating point sets, point bases and point skeletons. The main result is that the complement to any basis (skeleton) is a skeleton (basis).
Petrescu, Adrian (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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