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A Note on Root Decision Problems in Groups

Published online by Cambridge University Press:  20 November 2018

Seymour Lipschutz  and
Martin Lipschutz
Seymour Lipschutz
Affiliation:
Temple University, Philadelphia, Pennsylvania
Martin Lipschutz
Affiliation:
William Pater son College, Wayne, New Jersey
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 702 - 705
Copyright
Copyright © Canadian Mathematical Society 1973

References

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. Britton, J. L., Solution of the word problem for certain types of groups. I, Glasgow Math. J. 3 (1956), 45–54.Google Scholar
3. Lipschutz, S., On powers in generalized free products of groups, Arch. Math. (Basel) 19 (1968), 575–576.Google Scholar