Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unramified extensions of quadratic number fields with certain perfect
  Galois groups   We provide infinite families of quadratic number fields with everywhere
unramified Galois extensions of Galois group $SL_2(7)$ and $2.A_7$,
respectively. To my knowledge, these are the first instances of infinitely many
such realizations for perfect groups which are not generated by involutions, a
property which makes them difficult to approach for the problem in question and
leads to somewhat delicate local-global problems in inverse Galois theory.

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The categories of this paper are: physics
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat