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We describe types of double magma associated with Ward quasigroups, doubleWard quasigroups, their duals and the groups they generate. Ward quasigroupdouble magma and unipotent, right modular, left unital double magma are provedto be improper. Necessary and sufficient conditions are found on a pair ofright modular, left unital magma (and right-left unital magma) for them to forma double magma. We give further insight into the intimate connection betweenmediality and the interchange law by proving that a quasigroup is medial if andonly if any pair of its parastrophic binary operations satisfy the interchangelaw.

Double Magma associated with Ward and double Ward quasigroups