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Published online by Cambridge University Press: 20 November 2018
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  has shown that the word problem is solvable for the group with unsolvable conjugacy problem given by Novikov .