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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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For correspondence; e-mail: nik@mcs.st-and.ac.uk
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] I. M. Araújo and N. Ruškuc , ‘On finite presentability of direct products of semigroups’, Algebra Colloq. 7 (2000), 8391.

[3] P. Gallagher and N. Ruškuc , ‘On finite generations and presentability of Schützenberger products’, J. Aust. Math. Soc. 83 (2007), 357367.

[4] T. G. Lavers , ‘Presentations of general products’, J. Algebra 204 (1998), 733741.

[6] E. F. Robertson , N. Ruškuc and M. R. Thomson , ‘Finite generation and presentability of wreath products of monoids’, J. Algebra 266 (2003), 382392.

[7] E. F. Robertson , N. Ruškuc and J. Wiegold , ‘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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