A coalgebraic approach to quasigroup permutation representations. (Q1771959)

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.