Automorphisms of transformation semigroups

Abstract

We let X be an arbitrary non-empty set throughout. Many papers have been written describing the automorphisms of various transformation semigroups defined on X : total (Lyapin (1955), Magill (1967), Malcev (1952), Schreier (1936)), partial (Gluskin (1959), Magill (1967)), partial and 1–1 (Liber (1953)), partial and shifting at most a finite number of elements (Subov (1961a)). In all these cases the automoprhisms are shown to be “inner”, and using the fact this authors deduce that the automorphism group of the given transformation semigroup is isomorphic to the group g x of all permutations defined on X .