Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The abelian monoid of fusion-stable finite sets is free   We show that the abelian monoid of isomorphism classes of G-stable finite
S-sets is free for a finite group G with Sylow p-subgroup S; here a finite
S-set is called G-stable if it has isomorphic restrictions to G-conjugate
subgroups of S. These G-stable S-sets are of interest, e.g., in homotopy
theory. We prove freeness by constructing an explicit (but somewhat
non-obvious) basis, whose elements are in one-to-one correspondence with the
G-conjugacy classes of subgroups in S. As a central tool of independent
interest, we give a detailed description of the embedding of the Burnside ring
for a saturated fusion system into its associated ghost ring.

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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: econ