On the determination of Green's relations in finite transformation semigroups

This paper contains an algorithm which, on input the set of generators of a transformation semigroup S on a finite set, gives all Green's relations on S, a set of generators for the maximal subgroups of S, and a complete determination of the partially ordered set of all the -classes of S.The algorithm is based on an earlier technique of J. F. Perrot for studying regular -classes and on new results on non-regular -classes allowing for a systematic search for all the -classes of S