Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantitative Neumann lemma for finitely generated groups   We study the coset covering function $\mathfrak{C}(r)$ of a finitely
generated group: the number of cosets of infinite index subgroups needed to
cover the ball of radius $r$. We show that $\mathfrak{C}(r)$ is linear for
virtually nilpotent groups, exponential for property (T) groups, and is of
order at least $\sqrt{r}$ for all groups.

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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg