Monatshefte für Mathematik

, Volume 134, Issue 4, pp 287–293 | Cite as

Comparing Semigroup and Monoid Presentations for Finite Monoids

  • C. M. Campbell
  • J. D. Mitchell
  • N. Ruškuc

Abstract.

 It is known that for any finite group G given by a finite group presentation \(\) there exists a finite semigroup presentation \(\) for G of the same deficiency, i.e. satisfying \(\). It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and sufficient condition for a finite monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.

2000 Mathematics Subject Classification: 20M05 
Key words: Semigroup presentations monoid presentations deficiency 

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Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • C. M. Campbell
    • 1
  • J. D. Mitchell
    • 1
  • N. Ruškuc
    • 1
  1. 1.University of St. Andrews, ScotlandGB

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