Classification of Osborn loops of order 4n

Resumen

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.

Biografía del autor

Abednego O. Isere, Ambrose Alli University.
Department of Mathematics, Faculty of Physical Sciences.
J. O. Adéniran, Federal University of Agriculture.
Department of Mathematics.
T. G. Jaiyéolá, Obafemi Awolowo University.
Department of Mathematics.

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Publicado
2019-02-25
Cómo citar
Isere, A., Adéniran, J., & Jaiyéolá, T. (2019). Classification of Osborn loops of order 4n. Proyecciones. Revista De Matemática, 38(1), 31-47. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/3410
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