Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The commutator subgroup of the braid group is generated by two elements   For $n$ at least 7 and $n$ equal to 5, we give generating sets of size 2 for
the commutator subgroup of the braid group on $n$ strands. These generating
sets are of the smallest possible cardinality. For $n$ equal to 4 or 6, we give
generating sets of size three. We also prove that the commutator subgroup of
the braid group on 4 strands cannot be generated by fewer than three elements.

21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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The categories of this paper are: econ
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom