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Published online by Cambridge University Press: 09 April 2009
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.