ON THE DETERMINATION OF GREENS 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 (Figure presented.)-classes of S. The algorithm is based on an earlier technique of J. F. Perrot for studying regular (Figure presented.)-classes and on new results on non-regular (Figure presented.)-classes allowing for a systematic search for all the (Figure presented.)-classes of S. © 1990, Academic Press Limited. All rights reserved.