Quantifying Residual Finiteness

Details Quantifying Residual Finiteness Quantifying Residual Finiteness

2008-07-06

arxiv.org/abs/0807.0862v7

K. Bou-Rabee, \emph{Quantifying residual finiteness}, J. Algebra, {\bf 323} (2010), 729--737

Mathematics

Group Theory

11 pages, 0 figures, streamlined proof of Theorem 2.4

Scientific paper

10.1016/j.jalgebra.2009.10.008

We introduce the concept of quantifying the extent to which a finitely generated group is residually finite. The quantification is carried out for some examples including free groups, the first Grigorchuk group, finitely generated nilpotent groups, and certain arithmetic groups such as $SL_n(\mathbb{Z})$. In the context of finite nilpotent quotients, we find a new characterization of nilpotent groups.

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