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Unsolvable Problems in Groups With Solvable Word Problem

Published online by Cambridge University Press:  20 November 2018

James McCool
James McCool*
Affiliation:
University of Toronto, Toronto, Ontario
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Let G be a finitely presented group with solvable word problem. It is of some interest to ask which other decision problems must necessarily be solvable for such a group. Thus it is easy to see that there exist effective procedures to determine whether or not such a group is trivial, or nilpotent of a given class. On the other hand, the conjugacy problem need not be solvable for such a group, for Fridman [5] has shown that the word problem is solvable for the group with unsolvable conjugacy problem given by Novikov [9].

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 4 , 01 August 1970 , pp. 836 - 838
Copyright
Copyright © Canadian Mathematical Society 1970

References

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