Automorphisms of normal partial transformation semigroups

Abstract

We letXbe an arbitrary infinite set. A semigroupSof total or partial transformations ofXis called-normal ifhSh-1=S, for allhin, the symmetric group onX. For example, the full transformation semigroup, the semigroup of all partial transformations, the semigroup of all 1–1 partial transformationsand all ideals ofandare-normal.