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Some results concerning a transformation semigroup

Published online by Cambridge University Press:  09 April 2009

J. S. V. Symons
Affiliation:
University of Western AustraliaNedlands Western, Australia
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The full transformation semigroup F(X) is extremely important. As far back as 1952, Malcev (1952) showed that its automorphism group consisted of mappings of the form g-1 · g, g ∈ G(X). The present work is devoted to a generalization of this result.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

Clifford, A. H. and Preston, G. B. (1961, 1967), The algebraic theory of semigroups, Vols. I and II (Math. Surveys of the American Math. Soc., 7, 1961 and 1967).Google Scholar
Magill, K. D. Jr, (1966), ‘Subsemigroups of S(X)’, Math. Japon. 11, 109115.Google Scholar
Malcev, A. I. (1952), ‘Symmetric groupoids’, Mat. Sb. (N. S.) 13 (73), 136151.Google Scholar
Scott, W. R. (1964), Group Theory, (Prentice-Hall, 1964).Google Scholar
Sierpinski, W. (1958), Cardinal and Ordinal Numbers, (Warszawa, 1958).Google Scholar