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A Machine Program for Coset Enumeration

Published online by Cambridge University Press:  20 November 2018

H. F. Trotter
H. F. Trotter*
Affiliation:
Princeton University
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 357 - 368
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
5. Schreier, O., Die Untergruppen der freien Gruppen, Hamb. Abh., 5 (1926), 161–183.Google Scholar