Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-10T04:53:00.717Z Has data issue: false hasContentIssue false
  • English
  • Français

The order problem and the power problem for free product sixth-groups

Published online by Cambridge University Press:  18 May 2009

James McCool
James McCool
Affiliation:
University of Toronto, Toronto, Canada
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.

Let G be a group given in terms of generators and denning relations. The order problem is said to be solvable for (the given presentation of) the group G if, given any element W of G (as a word in the given generators of G), we can determine the order of W in G. The power problem is solvable for G if, given any pair X, Y of elements of G, we can determine whether or not X belongs to the cyclic subgroup {Y} of G generated by Y. It is easy to see that if either of these problems is solvable for G, then the word problem is also solvable for G.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 1 , January 1969 , pp. 1 - 9
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

1.Boone, W. W., The word problem, Ann. of Math. 70 (1959), 207–265.CrossRefGoogle Scholar
2.Britton, J. L., Solution of the word problem for certain types of groups I, Proc. Glasgow Math. Assoc. 3 (1956), 45–54.CrossRefGoogle Scholar
3.Britton, J. L., Solution of the word problem for certain types of groups II, Proc. Glasgow Math. Assoc. 3 (1956), 68–90.CrossRefGoogle Scholar
4.Greendlinger, M., On Dehn's algorithms for the conjugacy and word problems, with applications, Comm. Pure Appl. Math. 13 (1960), 641–677.CrossRefGoogle Scholar
5.Higman, G., Subgroups of finitely presented groups, Proc. Roy. Soc. A262 (1961), 455–475.Google Scholar
6.Lipschutz, S., An extension of Greendlinger's results on the word problem, Proc. Amer. Math. Soc. 15 (1964), 37–43.Google Scholar
7.McCool, J., Elements of finite order in free product sixth-groups, Glasgow Math. J. 9 (1968), 128–145.CrossRefGoogle Scholar