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Some Remarks on Semigroup Presentations

Published online by Cambridge University Press:  20 November 2018

B. H. Neumann
B. H. Neumann*
Affiliation:
The Australian National University, Canberra
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Let a semigroup A be given by generators a1, a2, … , ad and defining relations u1 = v1, u2 = v2, … , ue = ve between these generators, the ui, vi being words in the generators. We then have a presentation of A, and write

The same generators with the same relations can also be interpreted as the presentation of a group, for which we write

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1018 - 1026
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F. 14 (1st ed., Berlin-Göttingen-Heidelberg, 1957; 2nd éd., Berlin-Göttingen-Heidelberg-New York, 1965).Google Scholar
2. Mennicke, Jens, Einige endliche Gruppen mit drei Erzeugenden und drei Relationen, Arch. Math., 10 (1959), 409–418.Google Scholar
3. Neumann, B. H., Adjunction of elements to groups, J. London Math. Soc., 18 (1943), 4–11.Google Scholar
4. Neumann, B. H., An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London, A, 246 (1954), 503–554.Google Scholar
5. Neumann, B. H., On some finite groups with trivial multiplicator, Publ. Math. Debrecen, 4 (1956), 190–194.Google Scholar
6. Neumann, B. H., Embedding theorems for semigroups, J. London Math. Soc., 35 (1960), 184–192.Google Scholar
7. Todd, J. A. and Coxeter, H. S. M., A practical method for enumerating cosets of a finite abstract group, Proc. Edinburgh Math. Soc. (2), 5 (1936), 26–34.Google Scholar