REPRESENTATIONS OF FINITE OSBORN LOOPS

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.