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dc.rights.licenseAtribución-NoComercial 4.0 Internacional
dc.contributor.authorPereira Da Silva, Clovis
dc.contributor.authorKatsume MiyaóKa, Florinda
dc.description.abstractWe show relations among some classes of quasigroups. A quasigroup (G,.) is calIed unipotent if it contains an element x  such that a.a = x, for every a in G; subtractive  if b.(b.a) = a and a. (b.c) = c|.(b.a)  for all a,b,c in G; medial if (a.b).(c.d) =(a.c).(b.d) for all a,b,c,d in G. We define a Ward quasigroup as any quasigroup (G,.) containing an element i ϵ G such that a.a = i and (a.b).c = a.(c.(i.b)) for all a,b,c in G. A quasigroup (G,.) which contains an element i that satisfies the axioms a.x = b ↔ x = (i.b).(i.a) and y.a = b↔ y = b.(i.a) for all a,b in G, is called a Cardoso quasigroup by A. Sade [4]. If the class of the quasigroup is denoted by the initial letter of the respective name, then:(1) S ⊂W⊂C⊂U; (2) M∩C = S. There is no relation of inclusion between the class of loops and any of the other classes; we exhibit examples to evidence this fact. Furthermore, we establish necessary and sufficient conditions for a Cardoso quasigroup to be a loop.This paper is concerned with relations among the classes of the following quasigroups: subtractive, medial, Cardoso, Ward, unipotent and loop. In a sense, it is a continuation of [5], where some types of unipotent quasigroups were studied. Ward quasigroups are important because there is a conection between these quasigroups and groups [2]. Namely, if (G,.) is a Ward quasigroup, then (G,*) is a group under the operation * defined by a*b = a.(i.b); conversely, if (G,*) is agroup, then (G,.) is a Ward quasigroup with respect to the operation  defined by a.b = a*b-1. In particular, if thegroup (G,*) is abelian, then the quasigroup is subtractive.
dc.publisherUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
dc.relation.ispartofUniversidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
dc.relation.ispartofRevista Colombiana de Matemáticas
dc.relation.ispartofseriesRevista Colombiana de Matemáticas; Vol. 13, núm. 4 (1979); 311-321 0034-7426
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.titleRelations among some classes of quasigroups
dc.typeArtículo de revista
dc.relation.referencesPereira Da Silva, Clovis and Katsume MiyaóKa, Florinda (1979) Relations among some classes of quasigroups. Revista Colombiana de Matemáticas; Vol. 13, núm. 4 (1979); 311-321 0034-7426 .
dc.subject.proposalSome classes of quasigroups
dc.subject.proposalquasigroups subtractive

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