Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On groups whose geodesic growth is polynomial   This note records some observations concerning geodesic growth functions. If
a nilpotent group is not virtually cyclic then it has exponential geodesic
growth with respect to all finite generating sets. On the other hand, if a
finitely generated group $G$ has an element whose normal closure is abelian and
of finite index, then $G$ has a finite generating set with respect to which the
geodesic growth is polynomial (this includes all virtually cyclic groups).

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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas