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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, UKPeterg@mcs.st-and.ac.uknik@mcs.st-and.ac.uk
Nik Ruškucs
Affiliation:
School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsScotland, UKPeterg@mcs.st-and.ac.uknik@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

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