Upper Bounds on the Distance Between Groups and Quasi-groups

We introduce a new approach which makes it possible to compute upper bounds on the distance between groups and quasi-groups with the same underlying set. Our approach is based on the fact that the group (ℤp, +) can be transformed into a quasi-group by using a set of permutations. As an application we compute upper bounds on the distance when the number of elements in the underlying set is a small prime: for example, distance (101) ⩽ 26