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ON GENERATORS AND PRESENTATIONS OF SEMIDIRECT PRODUCTS IN INVERSE SEMIGROUPS

Part of: Semigroups

Published online by Cambridge University Press:  17 April 2009

E. R. DOMBI  and
N. RUŠKUC
E. R. DOMBI
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, UK (email: erzsi@mcs.st-and.ac.uk)
N. RUŠKUC*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland, UK (email: nik@mcs.st-and.ac.uk)
*
✉For correspondence; e-mail: nik@mcs.st-and.ac.uk
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Abstract

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In this paper we prove two main results. The first is a necessary and sufficient condition for a semidirect product of a semilattice by a group to be finitely generated. The second result is a necessary and sufficient condition for such a semidirect product to be finitely presented.

Keywords

inverse semigroupssemidirect productsgeneratorspresentationsgroupssemilatticesactions

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 20M30: Representation of semigroups; actions of semigroups on sets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 353 - 365
Copyright
Copyright © Australian Mathematical Society 2009

References

[1] Araújo, I. M. and Ruškuc, N., ‘On finite presentability of direct products of semigroups’, Algebra Colloq. 7 (2000), 83–91.CrossRefGoogle Scholar
[2] Dombi, E. R., ‘Automatic S-acts and inverse semigroup presentations’, PhD Thesis, University of St Andrews, St Andrews, Scotland, UK, 2004.Google Scholar
[3] Gallagher, P. and Ruškuc, N., ‘On finite generations and presentability of Schützenberger products’, J. Aust. Math. Soc. 83 (2007), 357–367.CrossRefGoogle Scholar
[4] Lavers, T. G., ‘Presentations of general products’, J. Algebra 204 (1998), 733–741.CrossRefGoogle Scholar
[5] Lawson, M. V., ‘Inverse semigroups’, The Theory of Partial Symmetries (World Scientific, River Edge, NJ, 1998).Google Scholar
[6] Robertson, E. F., Ruškuc, N. and Thomson, M. R., ‘Finite generation and presentability of wreath products of monoids’, J. Algebra 266 (2003), 382–392.CrossRefGoogle Scholar
[7] 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