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Recognizing powers in nilpotent groups and nilpotent images of free groups

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
Department of Mathematics and Computer Science City College of New York New York, N.Y. [email protected]
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Abstract

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An element in a free group is a proper power if and only if it is a proper power in every nilpotent factor group. Moreover there is an algorithm to decide if an element in a finitely generated torsion-free nilpotent group is a proper power.

MSC classification

Secondary: 20F18: Nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 2 , October 2007 , pp. 149 - 156
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Baumslag, G, Cannonito, F. B., Robinson, D. and Segal, D., ‘The algorithmic theory of polycyclic-by-finite groups’, J. Algebra 142 (1994), 118–149.CrossRefGoogle Scholar
[2]Hall, P., ‘Some sufficient condtions for a group to be nilpotent’, Illinois J. Math. 2 (1958), 787–801.CrossRefGoogle Scholar
[3]Kurosh, A. G., The theory of groups, vol. 2 (Chelsea, New York, 1960).Google Scholar
[4]Magnus, W., Karrass, A. and Solitar, D., Combinatorial group theory (Wiley, New York, 1966).Google Scholar
[5]Moran, S., ‘Errata and addenda to “A subgroup theorem for free nilpotent groups”’, Trans. Amer. Math. Soc. 112 (1964), 79–83.Google Scholar