# Classification of Osborn loops of order 4n

## Keywords:

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.

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## How to Cite

*Proyecciones (Antofagasta, On line)*, vol. 38, no. 1, pp. 31-47, Feb. 2019.