Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The infinite simple group V of Richard J. Thompson: presentations by
  permutations   We show that one can naturally describe elements of R. Thompson's finitely
presented infinite simple group $V$, known by Thompson to have a presentation
with four generators and fourteen relations, as products of permutations
analogous to transpositions. This perspective provides an intuitive explanation
towards the simplicity of $V$ and also perhaps indicates a reason as to why it
was one of the first discovered infinite finitely presented simple groups: it
is (in some basic sense) a relative of the finite alternating groups. We find a
natural infinite presentation for $V$ as a group generated by these
"transpositions," which presentation bears comparison with Dehornoy's infinite
presentation and which enables us to develop two small presentations for $V$: a
human-interpretable presentation with three generators and eight relations, and
a Tietze-derived presentation with two generators and seven relations.

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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-fin