A coalgebraic approach to quasigroup permutation representations.
The paper is devoted to permutation representations of finite quasigroups. The class of all permutation representations of a given finite quasigroup is identified with a covariety of coalgebras. Each permutation representation decomposes as a sum of homomorphic images of homogeneous spaces. For groups, permutation representations in the sense presented specialize to the classical concept. Also Burnside's Lemma is extended from groups to quasigroups.
scientific article; zbMATH DE number 2158819