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CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS

Part of: Semigroups

Published online by Cambridge University Press:  01 February 2008

ALAN J. CAIN ,
EDMUND F. ROBERTSON  and
NIK RUŠKUC
ALAN J. CAIN
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: alanc@mcs.st-and.ac.uk)
EDMUND F. ROBERTSON
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: edmund@mcs.st-and.ac.uk)
NIK RUŠKUC*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, 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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It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.)

Keywords

Maclev presentationcancellativesubsemigroupfinite indexrewriting

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 1 , February 2008 , pp. 39 - 61
Copyright
Copyright © 2008 Australian Mathematical Society

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