On another two cryptographic identities in universal Osborn loops.
Jaiyéọlá, T.G., Adéníran, J.O. (2010)
Surveys in Mathematics and its Applications
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Jaiyéọlá, T.G., Adéníran, J.O. (2010)
Surveys in Mathematics and its Applications
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Jaíyéọlá, Tèmítópé Gbóláhàn (2009)
Acta Universitatis Apulensis. Mathematics - Informatics
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Daniel Wagner, Stefan Wopperer (2007)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this article we construct proper Bol-loops of order using a generalisation of the semidirect product of groups defined by Birkenmeier and Xiao. Moreover we classify the obtained loops up to isomorphism.
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 -inverse loops and middle Bol loops.
V. S. Ramamurthi (1984)
Acta Universitatis Carolinae. Mathematica et Physica
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Phillips, J. D., Petr Vojtěchovský (2008)
Commentationes Mathematicae Universitatis Carolinae
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Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simplicity of axioms can be achieved for some of the most important varieties of loops. In particular, we investigate loops of Bol-Moufang type in the underlying variety of magmas with two-sided inverses, and obtain ``group-like'' equational bases for Moufang, Bol and C-loops. We also discuss the case when the inverses...