Global determinism of completely regular semigroups

Abstract

The power semigroup of a semigroup $ S $ is the semigroup of all nonempty subsets of $ S $ equipped with the naturally defined multiplication. A class $\mathcal{K} $ of semigroups is globally determined if any two members of $ \mathcal{K} $ with isomorphic globals are themselves isomorphic. The global determinability for various classes of semigroups has attracted some attention during the past 50 years. In this paper we prove that the class of all completely regular semigroups is globally determined. This is an extension and generalization of a series of related results obtained by some other mathematicians.