AUTOMORPHISM GROUPS OF ENDOMORPHISM MONOIDS OF FREE G-SETS

Abstract

Let G be a group. A G-set is a nonempty set A together with a (right) action of G on A. The class of G-sets, viewed as unary algebras, is a variety. For a set X, let AG(X) be the free algebra on X in the variety of G-sets. We determine the group of automorphisms of End (AG(X)), the monoid of endomorphisms of AG(X).