Resumen de A closure condition which is equivalent to the Thomsen condition in quasigroups

M. A. Taylor

• In this note it is shown that the closure condition, X1Y2 = X2Y1, X1Y4 = X2Y3, X3Y3 = X4Y1 --> X4Y2 = X3Y4, (and its dual) is equivalent to the Thomsen condition in quasigroups but not in general. Conditions are also given under which groupoids satisfying it are principal homotopes of cancellative, abelian semigroups, or abelian groups.