Geodesic
A Note on Root Decision Problems in Groups
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 702-705

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

Consider a positive integer r > 1. We say that the rth root problem is solvable for a group G if we can decide for any W ॉ G whether or not W has an rth root, i.e. whether or not there exists V ॉ G such that W = Vr.Baumslag, Boone and Neumann [1] proved that there exists a finitely presented group with all root problems unsolvable. Here we are concerned with the relationship between the different root problems. 
Lipschutz, Seymour; Lipschutz, Martin. A Note on Root Decision Problems in Groups. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 702-705. doi: 10.4153/CJM-1973-071-8
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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, Glasgow Math. J. 3 (1956), 45–54. Google Scholar

[3] 3. Lipschutz, S., On powers in generalized free products of groups, Arch. Math. (Basel) 19 (1968), 575–576. Google Scholar

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