J. Aust. Math. Soc. 83 (2007), no. 2, pp. 149–155.

Recognizing powers in nilpotent groups and nilpotent images of free groups

Gilbert Baumslag
Department of Mathematics and Computer Science
City College of New York
New York, N.Y. 10031
Received 1 March 2006; revised 23 May 2006
Communicated by C. F. Miller


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.

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2000 Mathematics Subject Classification: primary 20F18
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