QUASI-GROUPS AND QUANDLES

Two connexions between quasigroups and quandles are established. In one direction, Joyce's homogeneous quandle construction is shown to yield a quasigroup isotopic to the loop constructed by Scimemi on the set of phi-commutators of a group automorphism phi. In the other direction, the universal multiplication group construction of quasigroup theory is extended to quandles. The group of a knot becomes the universal right multiplication group of the knot quandle.