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Automorphisms of transformation semigroups

Published online by Cambridge University Press:  09 April 2009

R. P. Sullivan
R. P. Sullivan
Affiliation:
University of Western Australia, Nedlands, W. A. 6009
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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 gx of all permutations defined on X.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 1 , August 1975 , pp. 77 - 84
Copyright
Copyright © Australian Mathematical Society 1975

References

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