Comparing Semigroup and Monoid Presentations for Finite Monoids

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7 Citations (Scopus)


It is known that for any finite group G given by a finite group presentation (A\R) there exists a finite semigroup presentation <B\Q> for G of the same deficiency, i.e. satisfying \Q\ - \B\ = \R\ - \A\. 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.

Original languageEnglish
Pages (from-to)287-293
Number of pages7
JournalMonatshefte für Mathematik
Issue number4
Publication statusPublished - Feb 2002


  • semigroup presentations
  • monoid presentations
  • deficiency


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