Recognizing powers in nilpotent groups and nilpotent images of free groups

Recognizing powers in nilpotent groups and nilpotent images of free groups

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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Bibliographic Details
Published in:Journal of the Australian Mathematical Society (2001) Vol. 83; no. 2; pp. 149 - 156
Main Author: Baumslag, Gilbert
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01-10-2007
Subjects:
Algorithms
primary 20F18
primary 20F18
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Description
Summary: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.
Bibliography:ark:/67375/6GQ-WTQRQ98F-F
PII:S1446788700036843
istex:F8D415E60E59F6156F71DA722FFA5DEE969C873E
ArticleID:03684
ISSN:1446-7887
1446-8107
DOI:10.1017/S1446788700036843