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On finite generation and presentability of Schützenberger products

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Peter Gallagher  and
Nik Ruškucs
Peter Gallagher
Affiliation:
School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsScotland, [email protected]@mcs.st-and.ac.uk
Nik Ruškucs
Affiliation:
School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsScotland, [email protected]@mcs.st-and.ac.uk
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Abstract

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The finite generation and presentation of Schützenberger products of semigroups are investigated. A general necessary and sufficient condition is established for finite generation. The Schützenberger product of two groups is finitely presented as an inverse semigroup if and only if the groups are finitely presented, but is not finitely presented as a semigroup unless both groups are finite.

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 20M18: Inverse semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 3 , December 2007 , pp. 357 - 368
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Gomes, G. M. S.. Pin, J-E. and Sezinando, H., ‘Presentations of the Schützenberger product of n groups’, Comm. Algebra to appear.Google Scholar
[2]Gray, R. and Ruškuc, N., ‘Generators and relations for subsemigroups via boundaries in Cayley graphs’, submitted.Google Scholar
[3]Howie, J. M.. Automata and languages (Clarendon Press, Oxford, 1991).CrossRefGoogle Scholar
[4]Howie, J. M.. Fundamentals of Semigroup Theory, volume 12 of London Math. Soc. Monogr. Ser. (Clarendon Press. New York. 1995).CrossRefGoogle Scholar
[5]Howie, J. M. and Ruškuc, N.. ‘Constructions and presentations for monoids’, Comm. Algebra 22 (1994). 6209–6224.CrossRefGoogle Scholar
[6]Margolis, S. W. and Pin, J-E.. ‘Expansions, free inverse semigroups and Schützenberger product’. J. Algebra 110 (1987). 298–305.CrossRefGoogle Scholar
[7]Petrich, M., Inverse semigroups (John Wiley and Sons Publication, 1984).Google Scholar
[8]Robertson, E. F.. Ruškuc, N. and Wiegold, J.. ‘Generators and relations of direct products of semigroups’. Trans. Amer. Math. Soc. 350 (1998). 2665–2685.CrossRefGoogle Scholar
[9]Ruškuc, N.. Semigroup presentations (Ph.D. Thesis. University of St Andrews. 1995).Google Scholar
[10]Schein, B. M.. ‘Free inverse semigroups are not finitely presented’, Acta Math. Acad. Scient. Hung. 26 (1975). 41–52.CrossRefGoogle Scholar
[11]Schützenbergsr, M. P.. ‘On finite monoids having only trivial subgroups’, Information and Control 8(1965), 190–194.CrossRefGoogle Scholar