Hostname: page-component-54dcc4c588-rz4zl Total loading time: 0 Render date: 2025-09-22T04:51:01.546Z Has data issue: false hasContentIssue false
  • English
  • Français

An algorithm for determining defining relations of a subgroup

Published online by Cambridge University Press:  18 May 2009

D. H. McLain
D. H. McLain
Affiliation:
Computing Centre, University of Sheffield, Sheffield
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.

Suppose that G is a finitely presented group, and that we are given a set of generators for a subgroup H of finite index in G. In this paper we describe an algorithm by which a set of defining relations may be found for H in these generators.

The algorithm is suitable for programming on a digital computer. It appears to have significant computational advantages over the method of Mendelsohn [8] (which is based on the Schreier-Reidemeister results, see for example [4, pp. 91–95]) in those cases where the generators of H are given as other than the familiar Schreier-Reidemeister generators.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 51 - 56
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Benson, C. T. and Mendelsohn, N. S., A calculus for a certain class of word problems, J. Combinatorial Theory 1 (1966), 202–208.CrossRefGoogle Scholar
2.Leech, J., Coset enumeration on digital computers, Proc. Cambridge Philos. Soc. 59 (1963), 257–267.CrossRefGoogle Scholar
3.Leech, J. (ed.), Computational problems in abstract algebra (Pergamon, 1970).Google Scholar
4.Magnus, W., Karrass, A. and Solitar, D., Combinational group theory (Interscience, 1966).Google Scholar
5.McCarthy, J., Lisp 1.5 programmer's manual (MIT Press, 1968).Google Scholar
6.Mendelsohn, N. S., An algorithmic solution for a word problem in group theory, Canad. J. Math. 16 (1964), 509–516.CrossRefGoogle Scholar
7.Mendelsohn, N. S., Correction to: an algorithmic solution for a word problem in group theory, Canad. J. Math. 17 (1965), 505.CrossRefGoogle Scholar
8.Mendelsohn, N. S., Defining relations for subgroups of finite index of groups with a finite presentation, in reference [3] above, 43–44.Google Scholar
9.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.CrossRefGoogle Scholar
10.Wijngaarden, A. Van, Mailloux, B. J., Peck, J. E. L. and Koster, C. H. A., Report on the algorithmic language Algol 68, Numer. Math. 14 (1969), 79–218.Google Scholar