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Automorphisms of the semigroup of all onto mappings of a set

Published online by Cambridge University Press:  17 April 2009

Suchat Chantip  and
G.R. Wood
Suchat Chantip
Affiliation:
Department of Mathematics, Khon Kaen University, Khon Kaen, Thailand.
G.R. Wood
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
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Abstract

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The semigroup of all onto mappings of a set to itself and the semigroup of all one-to-one mappings of a set to itself are shown to have the property that every automorphism is inner.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 399 - 403
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Magill, Kenneth D. Jr., “Automorphisms of the semigroup of all relations on a set”, Canad. Math. Bull. 9 (1966), 73–77.CrossRefGoogle Scholar
[2]Schreier, J., “Über Abbildungen einer abstrakten Menge auf ihre Teilmengen”, Fund. Math. 28 (1937), 261–264.CrossRefGoogle Scholar
[3]Schreier, J. und Ulam, S., “Über die Automorphismen der Permutationsgruppe der natiirlichen Zahlenfolge”, Fund. Math. 28 (1937), 258–260.CrossRefGoogle Scholar