Computing automorphisms of semigroups

Authors:
J. Araújo;P. V. Bünau;J. D. Mitchell;M. Neunhöffer
Affiliations:
Universidade Aberta, R. da Escola Politécnica, 147, 1269-001 Lisboa, Portugal and Centro de Álgebra, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal;Technische Universität Berlin, Sekretariat FR 6-9, Franklinstr. 28/29, 10587 Berlin, Germany;Mathematics Department, University of St Andrews, Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS Scotland, United Kingdom;Mathematics Department, University of St Andrews, Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS Scotland, United Kingdom
Venue:
Journal of Symbolic Computation
Year:
2010

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Abstract

In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As applications of the algorithm all the automorphism groups of semigroups of order at most 7 and of the multiplicative semigroups of some group rings are found. We also consider which groups occur as the automorphism groups of semigroups of several distinguished types.