Heghine Ghumashyan, Jaroslav Guričan (2022)
Mathematica Bohemica
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We shall show that there exist sofic groups which are not locally embeddable into finite Moufang loops. These groups serve as counterexamples to a problem and two conjectures formulated in the paper by M. Vodička, P. Zlatoš (2019).
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''.
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.
Gábor P. Nagy (2008)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.
Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá, Bolaji Ajibola Popoola (2015)
Discussiones Mathematicae - General Algebra and Applications
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The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient conditions for the holomorph of a RIPL to be a Bol loop are deduced. Some...