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On semigroup presentations

Published online by Cambridge University Press:  20 January 2009

Edmund F. Robertson
Affiliation:
University of St AndrewsSt Andrews KY16 9SS, Scotland
Yusuf Ünlü
Affiliation:
Çukurova ÜniversitesiBalcali Adana, Turkey
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Abstract

Semigroup presentations have been studied over a long period, usually as a means of providing examples of semigroups. In 1967 B. H. Neumann introduced an enumeration method for finitely presented semigroups analogous to the Todd–Coxeter coset enumeration process for groups. A proof of Neumann's enumeration method was given by Jura in 1978.

In Section 3 of this paper we describe a machine implementation of a semigroup enumeration algorithm based on that of Neumann. In Section 2 we examine certain semigroup presentations, motivated by the fact that the corresponding group presentation has yielded interesting groups. The theorems, although proved algebraically, were suggested by the semigroup enumeration program.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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On semigroup presentations
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