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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

Information

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

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