Journal of the Australian Mathematical Society

Research Article

CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS

ALAN J. CAINa1, EDMUND F. ROBERTSONa2 and NIK RUŠKUCa3 c1

a1 School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: alanc@mcs.st-and.ac.uk)

a2 School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: edmund@mcs.st-and.ac.uk)

a3 School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK (email: nik@mcs.st-and.ac.uk)

Abstract

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.)

(Received September 29 2006)

(Revised May 17 2007)

2000 Mathematics subject classification

  • 20M05

Keywords and phrases

  • Maclev presentation;
  • cancellative;
  • subsemigroup;
  • finite index;
  • rewriting

Correspondence:

c1 For correspondence; e-mail: nik@mcs.st-and.ac.uk