Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutator width in the first Grigorchuk group   Let $G$ be the first Grigorchuk group. We show that the commutator width of
$G$ is $2$: every element $g\in [G,G]$ is a product of two commutators, and
also of six conjugates of $a$. Furthermore, we show that every finitely
generated subgroup $H\leq G$ has finite commutator width, which however can be
arbitrarily large, and that $G$ contains a subgroup of infinite commutator
width. The proofs were assisted by the computer algebra system GAP.

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The categories of this paper are: stat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex