Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-time isomorphism testing of groups of most finite orders   [PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian
groups and finite meta-cyclic groups. We prove that for a dense set of positive
integers $n$, isomorphism testing for abelian groups of black-box type of order
$n$ can be done in time polynomial in $\log n$. We also prove that for a dense
set of orders $n$ with given prime factors, one can test isomorphism for
coprime meta-cyclic groups of black-box type of order $n$ in time polynomial in
$\log n$. Prior methods for these two classes of groups have running times
exponential in $\log n$.

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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: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th