Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Irreducible, Infinite, Non-affine Coxeter Groups   The following results are proved: The center of any finite index subgroup of
an irreducible, infinite, non-affine Coxeter group is trivial; Any finite index
subgroup of an irreducible, infinite, non-affine Coxeter group cannot be
expressed as a product of two nontrivial subgroups. These two theorems imply a
unique decomposition theorem for a class of Coxeter groups. We also obtain that
the orbit of each element other than the identity under the conjugation action
in an irreducible, infinite, non-affine Coxeter group is an infinite set. This
implies that an irreducible, infinite Coxeter group is affine if and only if it
contains an abelian subgroup of finite index.

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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph