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Coset Enumeration in a Finitely Presented Semigroup

Published online by Cambridge University Press:  20 November 2018

Andrzej Jura
Andrzej Jura*
Affiliation:
Institute of Mathematics, technical university, Warsaw
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The enumeration method for finite groups, the so-called Todd-Coxeter process, has been described in [2], [3]. Leech [4] and Trotter [5] carried out the process of coset enumeration for groups on a computer. However Mendelsohn [1] was the first to present a formal proof of the fact that this process ends after a finite number of steps and that it actually enumerates cosets in a group. Dietze and Schaps [7] used Todd-Coxeter′s method to find all subgroups of a given finite index in a finitely presented group. B. H. Neumann [8] modified Todd-Coxeter′s method to enumerate cosets in a semigroup, giving however no proofs of the effectiveness of this method nor that it actually enumerates cosets in a semigroup.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 1 , 01 March 1978 , pp. 37 - 46
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Mendelsohn, N. S., An algorithmic solution for a word problem in group theory, Math.Can J. 16 (1964), p. 509-516. la., Correction, Can. J. Math. 17 (1965), p.505.Google Scholar
2. Coxeter, H. S. M and Moser, W. O. J., Generators and relations for discrete groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Chapter 2, 12-18.Google Scholar
3. Todd, J. A. and Coxeter, H. S. M., A practical method for enumerating cosets of a finite abstract groups, Proc. Edinburgh Math. Soc, (2), 5 (1936), 34-36.Google Scholar
4. John Leech, Coset enumeration on digital computers, Proc. Camb. Phil. Soc. 59 (1963), 257-267.Google Scholar
5. Trotter, H., An algorithm for the Todd-Coxeter method of coset enumeration, Canad. Math. Bull. 7 (1964), 357-368.Google Scholar
6. Marshall Hall, The theory of groups, (New York, 1959), Chapter 7.Google Scholar
7. Dietze, A. and Schaps, M., Determining subgroups of a given finite index in a finitely presented group, Can. J. Math. 26 (1974) pp. 769-782.Google Scholar
8. Neumann, B. H., Some remarks on semigroup presentations, Can. J. Math. 19 (1967) pp. 1018-1026.Google Scholar