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If $(G,·)$ is a group, and the operation $(*)$ is defined by $x*y=x·y^{-1}$ then by direct verification $(G,*)$ is a quasigroup which satisfies the identity $(x*y)*(z*y)=x*z$. Conversely, if one starts with a quasigroup satisfying the latter identity the group $(G,·)$ can be constructed, so that in effect $(G,·)$ is determined by its right division operation. Here the analogous situation is examined for a Moufang loop. Subtleties arise which are not present in the group case since there is a choice of defining identities and the identities produced by...