Classification of Osborn loops of order 4n

Abstract The smallest non-associative Osborn loop is of order 16. Attempts in the past to construct higher orders have been very difficult. In this paper, some examples of finite Osborn loops of order 4n, n = 4, 6, 8, 9, 12, 16 and 18 were presented. The orders of certain elements of the examples we...

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Autores principales:	Isere,Abednego O., Adéniran,J. O., Jaiyéolá,T. G.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2019
Materias:	Osborn loops order 4n classification examples isomorphism
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000100031
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spelling	oai:scielo:S0716-091720190001000312019-02-08Classification of Osborn loops of order 4nIsere,Abednego O.Adéniran,J. O.Jaiyéolá,T. G. Osborn loops order 4n classification examples isomorphism Abstract The smallest non-associative Osborn loop is of order 16. Attempts in the past to construct higher orders have been very difficult. In this paper, some examples of finite Osborn loops of order 4n, n = 4, 6, 8, 9, 12, 16 and 18 were presented. The orders of certain elements of the examples were considered. The nuclei of two of the examples were also obtained and these were used to establish the classification of these Osborn loops up to isomorphism. Moreover, the central properties of these examples were examined and were all found to be having a trivial center and no non-trivial normal subloop. Therefore, these examples of Osborn loops are simple Osborn loops.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.1 20192019-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000100031en10.4067/S0716-09172019000100031
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Osborn loops order 4n classification examples isomorphism
spellingShingle	Osborn loops order 4n classification examples isomorphism Isere,Abednego O. Adéniran,J. O. Jaiyéolá,T. G. Classification of Osborn loops of order 4n
description	Abstract The smallest non-associative Osborn loop is of order 16. Attempts in the past to construct higher orders have been very difficult. In this paper, some examples of finite Osborn loops of order 4n, n = 4, 6, 8, 9, 12, 16 and 18 were presented. The orders of certain elements of the examples were considered. The nuclei of two of the examples were also obtained and these were used to establish the classification of these Osborn loops up to isomorphism. Moreover, the central properties of these examples were examined and were all found to be having a trivial center and no non-trivial normal subloop. Therefore, these examples of Osborn loops are simple Osborn loops.
author	Isere,Abednego O. Adéniran,J. O. Jaiyéolá,T. G.
author_facet	Isere,Abednego O. Adéniran,J. O. Jaiyéolá,T. G.
author_sort	Isere,Abednego O.
title	Classification of Osborn loops of order 4n
title_short	Classification of Osborn loops of order 4n
title_full	Classification of Osborn loops of order 4n
title_fullStr	Classification of Osborn loops of order 4n
title_full_unstemmed	Classification of Osborn loops of order 4n
title_sort	classification of osborn loops of order 4n
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000100031
work_keys_str_mv	AT isereabednegoo classificationofosbornloopsoforder4n AT adeniranjo classificationofosbornloopsoforder4n AT jaiyeolatg classificationofosbornloopsoforder4n
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Classification of Osborn loops of order 4n

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