Some Examples Of Finite Osborn Loops

Abstract

In this work we give a number of constructions of finite Osborn loops of order 4n, with two generators. All the loops are found to satisfy both Langrange’s theorem and Sylow’s first theorem. They are found to be non-universal Osborn loops except when k = 1 and n ≤ 3. Moreover, all the examples are found not to be flexible and do not have the LAP or RAP or LIP or RIP or AAIP, consequently not Moufang. The first three cases are particular examples for demonstration purpose. Therefore, finite Osborn loops of order 16, 24, 36, 48 and 72 has been constructed.