Homomorphisms between Stone-Cech Homomorphisms into Stone-Cech Remainders of Countable Groups

Abstract

We study properties of continuous homomorphisms from β S into T* and from S* into T*, where S denotes a countably infinite semigroup and T denotes a countably infinite group. We show that they have striking algebraic properties if they do not arise as continuous extensions of homomorphisms from S to T.