On a generalization of the transformation semigroup

Abstract

In a series of papers ((1967), (1967a) and (1967b)) Magill has considered the semigroups J ( X, Y ; θ ) (definition below), a natural, but extensive, generalization of the usual transformation semigroup J ( X ). They have also been studiedin Sullivan (to appear). Under the assumption that θ be onto Magill described their automorphisms and determined when one J ( X, Y ; θ ) is isomorphic to another.