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GENERAL THEOREMS ON AUTOMORPHISMS OF SEMIGROUPS AND THEIR APPLICATIONS

Part of: Semigroups

Published online by Cambridge University Press:  01 August 2009

JOÃO ARAÚJO  and
JANUSZ KONIECZNY
JOÃO ARAÚJO
Affiliation:
Universidade Aberta, R. Escola Politécnica, 147, 1269-001 Lisboa, Portugal Centro de Álgebra, Universidade de Lisboa, 1649-003 Lisboa, Portugal (email: jarauja@ptmat.fc.ul.pt)
JANUSZ KONIECZNY*
Affiliation:
Department of Mathematics, University of Mary Washington, Fredericksburg, VA 22401, USA (email: jkoniecz@umw.edu)
*
✉For correspondence; e-mail: jkoniecz@umw.edu
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Abstract

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We introduce the notion of a strong representation of a semigroup in the monoid of endomorphisms of any mathematical structure, and use this concept to provide a theoretical description of the automorphism group of any semigroup. As an application of our general theorems, we extend to semigroups a well-known result concerning automorphisms of groups, and we determine the automorphism groups of certain transformation semigroups and of the fundamental inverse semigroups.

Keywords

automorphismsemigroupmonoid of endomorphismsrepresentation

MSC classification

Secondary: 20M15: Mappings of semigroups 20M30: Representation of semigroups; actions of semigroups on sets
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 1 , August 2009 , pp. 1 - 17
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The first author was partially supported by FCT and FEDER, Project POCTI-ISFL-1-143 of Centro de Algebra da Universidade de Lisboa, and by FCT and PIDDAC through the project PTDC/MAT/69514/2006.

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