Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brou\'e's Conjecture for 2-blocks with elementary abelian defect groups
  of order 32   The first author has recently classified the Morita equivalence classes of
2-blocks B of finite groups with elementary abelian defect group of order 32.
In all but three cases he proved that the Morita equivalence class determines
the inertial quotient of B. We finish the remaining cases by utilizing the
theory of lower defect groups. As a corollary, we verify Brou\'e's Abelian
Defect Group Conjecture in this situation.

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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con