Characters of finite quasigroups VII: permutation characters
Each homogeneous space of a quasigroup affords a representation of the Bose-Mesner algebra of the association scheme given by the action of the multiplication group. The homogeneous space is said to be faithful if the corresponding representation of the Bose-Mesner algebra is faithful. In the group case, this definition agrees with the usual concept of faithfulness for transitive permutation representations. A permutation character is associated with each quasigroup permutation representation,...