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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
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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.

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

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