Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and its normal closure   We determine the $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and
$K=\mathbb{Q}(\sqrt[3]{p},\sqrt{-3})$ when $p\equiv 4,7\bmod 9$ is a prime and
$3$ is a cubic modulo $p$. This confirms a conjecture made by Barrucand-Cohn,
and proves the last remaining case of a conjecture of Lemmermeyer on the
$3$-class group of $K$.

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The categories of this paper are: eess
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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th