జర్నల్ ఆఫ్ జెనరలైజ్డ్ లై థియరీ అండ్ అప్లికేషన్స్

Construction of Right Cheban Loops of Small Order

Abstract

AI Chinaka*, AO Abdulkareem and JO Aden?ran

In this study, we give constructions of right cheban loops of order 4t, using a multiplication defined on cartesian product of (C_2t X C₂) where C_2t is a cyclic group of order 2t, t is a positive integer: 3,4 and 6 and C₂ is a cyclic group of order 2, each gives a right cheban loop of orders 12, 16 and 24. It was found that smallest non-associative right cheban loop is of order 12 and finite examples of right cheban loops of orders 12,16 and 24 are generated as shown in the cayley tables.