REPRESENTATIONS OF FINITE OSBORN LOOPS

Authors

  • A. O. ISERE DEPARTMENT OF MATHEMATICS, AMBROSE ALLI UNIVERSITY, EKPOMA 310001, NIGERIA
  • J. O. ADÉNÍRAN DEPARTMENT OF MATHEMATICS, FEDERAL UNIVERSITY OF AGRICULTURE, ABEOKUTA 110101, NIGERIA MATHEMATICS PROGRAMME NATIONAL MATHEMATICAL CENTRE, ABUJA, NIGERIA
  • A. A. A. AGBOOLA DEPARTMENT OF MATHEMATICS, FEDERAL UNIVERSITY OF AGRICULTURE, ABEOKUTA 110101, NIGERIA

Abstract

It is shown that an Osborn loop of order n has n/2 generators. Given the determining permutations, the rep- resentation Π is generated by R(2) ◦ R(2 + i) = R(3 + i)∀i = 1, 3, 5, ..., n − 3. The representation of Osborn loops of order 16 is presented and it is used as an example to verify the results.  It is also shown that the order of every element of the representation Π divides the order of the loop, hence, Osborn loops of order 16 are langrangelike.

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Published

2017-01-28

How to Cite

ISERE, A. O., ADÉNÍRAN J. O., & AGBOOLA, A. A. A. (2017). REPRESENTATIONS OF FINITE OSBORN LOOPS. Journal of the Nigerian Mathematical Society, 35(2), 381–389. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/36

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