Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T12:27:08.392Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the Todd-Coxeter coset enumeration algorithm

Published online by Cambridge University Press:  20 January 2009

M. J. Beetham  and
C. M. Campbell
M. J. Beetham
Affiliation:
Mathematical Institute, University of St Andrews
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In (8) Todd and Coxeter described an algorithm for enumerating the cosets of a finitely generated subgroup of finite index in a finitely presented group. Several authors ((1), (2), (5), (6), (7)) have discussed a modification of the algorithm to give also a presentation of the subgroup in terms of the given generators.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 1 , March 1976 , pp. 73 - 79
Copyright
Copyright © Edinburgh Mathematical Society 1976

References

REFERENCES

(1) Benson, C. T. and Mendelsohn, N. S., A calculus for a certain class of word problems in groups, J. Combinatorial Theory 1 (1966), 202–208.CrossRefGoogle Scholar
(2) Campbell, C. M., Dissertation, McGill University, 1965.Google Scholar
(3) Campbell, C. M. and Robertson, E. F., Remarks on a class of 2-generator groups of deficiency zero, J. Australian Math. Soc. 19 (1975), 297–305.CrossRefGoogle Scholar
(4) Campbell, C. M. and Robertson, E. F., The orders of certain metacyclic groups, Bull. London Math. Soc. 6 (1974), 312–314.CrossRefGoogle Scholar
(5) Cannon, J. J., Dimino, L. A., Havas, G. and Watson, J. M., Implementation and analysis of the Todd-Coxeter algorithm, Math. Comp. 11 (1973), 463–490.CrossRefGoogle Scholar
(6) Leech, J., Computer proof of relations in groups, Proceedings of the Royal Irish Academy Summer School on Group Theory and Computation (Academic Press, to appear).Google Scholar
(7) Mendelsohn, N. S., Defining relations for subgroups of finite index of groups with a finite presentation, Computational Problems in Abstract Algebra edited by J. Leech (Pergamon, Oxford, 1970), 43–44.Google Scholar
(8) Todd, J. A. and Coxeter, H. S. M.A practical method for enumerating cosets of a finite abstract group, Proc. Edinburgh Math. Soc. 5 (1936), 26–34.CrossRefGoogle Scholar