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ON GENERATORS AND PRESENTATIONS OF SEMIDIRECT PRODUCTS IN INVERSE SEMIGROUPS

  • E. R. DOMBI (a1) and N. RUŠKUC (a2)
Abstract
Abstract

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.

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Copyright
Corresponding author
For correspondence; e-mail: nik@mcs.st-and.ac.uk
References
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[1] Araújo I. M. and Ruškuc N., ‘On finite presentability of direct products of semigroups’, Algebra Colloq. 7 (2000), 8391.
[2] Dombi E. R., ‘Automatic S-acts and inverse semigroup presentations’, PhD Thesis, University of St Andrews, St Andrews, Scotland, UK, 2004.
[3] Gallagher P. and Ruškuc N., ‘On finite generations and presentability of Schützenberger products’, J. Aust. Math. Soc. 83 (2007), 357367.
[4] Lavers T. G., ‘Presentations of general products’, J. Algebra 204 (1998), 733741.
[5] Lawson M. V., ‘Inverse semigroups’, The Theory of Partial Symmetries (World Scientific, River Edge, NJ, 1998).
[6] Robertson E. F., Ruškuc N. and Thomson M. R., ‘Finite generation and presentability of wreath products of monoids’, J. Algebra 266 (2003), 382392.
[7] Robertson E. F., Ruškuc N. and Wiegold J., ‘Generators and relations of direct products of semigroups’, Trans. Amer. Math. Soc. 350 (1998), 26652685.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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