Finitely generated residually torsion-free nilpotent groups. I

Gilbert Baumslag

Type: Article

Publication Date: 1999-12-01

Citations: 9

DOI: https://doi.org/10.1017/s1446788700002032

Abstract

Abstract 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.

Locations

Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics - View - PDF

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Works Cited by This (19)

Action	Title	Year	Authors
+	Growth of Algebras and Gelfand-Kirillov Dimension	1999	Günter Krause T. H. Lenagan
+	Musings on Magnus	1994	Gilbert Baumslag
+	On generalised free products	1962	Gilbert Baumslag
+ PDF Chat	Conjugacy in nilpotent groups	1965	Norman Blackburn
+	Wreath products and varieties of groups	1962	Bernhard Neumann Hanna Neumann Peter Neumann
+ PDF Chat	Growth functions for residually torsion-free nilpotent groups	1990	Roger C. Alperin Brian L. Peterson
+	Introduction To Commutative Algebra	2018	Michael Atiyah
+	The residual nilpotence of the multiplicative group of a skew field generated by universal enveloping algebras	1988	A. I. Lichtman
+	Free Rings and Their Relations.	1973	David J. Fieldhouse P. M. Cohn
+	Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring	1935	Wilhelm Magnus