Elsevier

Journal of Algebra

Volume 175, Issue 1, 1 July 1995, Pages 105-121
Journal of Algebra

Regular Article
Groups of Polynomial Growth and Their Associated Metric Spaces

https://doi.org/10.1006/jabr.1995.1177Get rights and content
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Abstract

Let YN be the space associated with a finitely generated group G and a nonstandard natural number N. We prove the following two results. If YN is locally compact and has finite Minkowski dimension, then G is nilpotent-by-finite. If G is nilpotent, then YN is homeomorphic to Rn, where n is the sum of the ranks of the descending central series of G.

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