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Finitely generated residually torsion-free nilpotent groups. I

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 City College of New YorkNew York, NY 10031, USA
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Abstract

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The object of this paper is to study the sequence of torsion-free ranks of the quotients by the terms of the lower central series of a finitely generated group. This gives rise to the introduction into the study of finitely generated, residually torison-free nilpotent groups of notions relating to the Gelfand-Kirillov dimension. These notions are explored here. The main result concerning the sequences alluded to is the proof that there are continuously many such sequences.

Keywords

Residually torsion-free nilpotent groupsmetabelian groupsalgorithms

MSC classification

Secondary: 20F18: Nilpotent groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 67 , Issue 3 , December 1999 , pp. 289 - 317
Copyright
Copyright © Australian Mathematical Society 1999

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