Geodesic
Unsolvable Problems in Groups With Solvable Word Problem
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 836-838

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
McCool, James. Unsolvable Problems in Groups With Solvable Word Problem. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 836-838. doi: 10.4153/CJM-1970-094-6
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[1] 1. Baumslag, G., Boone, W. W., and Neumann, B. H., Some unsolvable problems about elements and subgroups of groups, Math. Scand. 7 (1959), 191–201. Google Scholar

[2] 2. Britton, J. L., Solution of the word problem for certain types of groups. I, Proc. Glasgow Math. Assoc. 3 (1956), 45–54. Google Scholar

[3] 3. Clapham, C. R. J., Finitely presented groups with word problems of arbitrary degree of insolubility, Proc. London Math. Soc. (3) 14 (1964), 633–676. Google Scholar

[4] 4. Clapham, C. R. J., An embedding theorem for finitely presented groups, Proc. London Math. Soc. (3) 17 (1967), 419–430. Google Scholar

[5] 5. Fridman, A. A., On the relation between the word problem and the conjugacy problem infinitely defined groups, Trudy Moskov. Mat. Obsc. 9 (1960), 329–365. (Russian) Google Scholar

[6] 6. Higman, G., Subgroups of finitely presented groups, Proc. Roy. Soc. Ser. A 262 (1961), 455–475. Google Scholar

[7] 7. McCool, J., The order problem and the power problem for free product sixth-groups, Glasgow Math. J. 10 (1969), 1–9. Google Scholar

[8] 8. McCool, J., Embedding theorems for countable groups, Can. J. Math. 22 (1970), 827–835. Google Scholar

[9] 9. Novikov, P. S., Unsolvability of the conjugacy problem in the theory of groups, Izv. Akad. Nauk SSSR Ser. Mat. 18 (1954), 485–524. (Russian) Google Scholar

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