No CrossRef data available.
Article contents
A Machine Program for Coset Enumeration
Published online by Cambridge University Press: 20 November 2018
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.
We are concerned with an algorithm for determining the index (when it is finite) of a subgroup H of a group K when K is specified by a finite set of generators and relations and H is specified as generated by a finite set of words in the generators of K. A systematic computational attack on the problem was discovered by Coxeter and Todd [l], and has proved to be a very useful tool in problems involving generators and relations in groups [2]. Although the method was not completely formalized it was clearly possible to convert it into a computer program, and this has been done by a number of people. Leech has given a survey of this work in [3], where further references may be found.
Information
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1964
References
1.
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
2.
Coxeter, H.S.M. and Moser, W.O.J., Generators and relations for discrete groups, Ergebnisse der Math.
14 (Springer;Berlin, 1957).Google Scholar
3.
Leech, J., Coset enumeration on digital computers, Proc. Camb. Phil. Soc.
59 (1963), 257–267.Google Scholar
4.
Mendelsohn, N. S., An algorithmic solution for a word problem in group theory, Dept. of Math. Publications, Univ. of Manitoba, 1963.Google Scholar
You have
Access
- 7
- Cited by