On non-isomorphic quasigroups of small order

Abstract

A non-empty set G is said to be a groupoid relatively to a binary operation denoted by {•}, if for every ordered pair (a, b) of elements of G there is a unique element ab ∈ G. A groupoid (G, •) is called a quasigroup if for every a, b ∈ G the equations a • x = b and y • a = b have unique solutions. A quasigroup (G, •) is called a Ward quasigroup if it satisfies the law (a • c) • (b • c) = a • b for all a, b, c ∈ G.