Quasigroup actions: Markov chains, pseudoinverses, and linear representations (Q1964675)

This paper initiates the extension to quasigroups of a further aspect of group representation theory: transitive permutation representations. Using pseudoinverses of incidence matrices of quasigroups in partitions induced by left multiplications of subquasigroups, a transitive permutation action of a quasigroup is defined as a set of Markov chain actions indexed by the quasigroup. Finally, Burnside's lemma for transitive quasigroup actions is derived.