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.
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(Received 17 April 2001; in revised form 15 September 2001)
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Campbell, C., Mitchell, J. & Ruškuc, N. Comparing Semigroup and Monoid Presentations for Finite Monoids. Mh Math 134, 287–293 (2002). https://doi.org/10.1007/s605-002-8263-7
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DOI: https://doi.org/10.1007/s605-002-8263-7