Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hilbert's class field and the p-class group of the cyclotomic fields   Let $p$ be an irregular prime and $K=\Q(\zeta)$ the $p$-cyclotomic field. Let
$\sigma$ be a $\Q$-isomorphism of $K$ generating $Gal(K/\Q)$. Let $S/K$ be a
cyclic unramified extension of degree $p$, defined by $S= K(A^{1/p})$ where
$A\in K\backslash K^p$, $A\Z_K=\mk a^p$ with $\mk a$ non-principal ideal of
$\Z_K$, $A^{\sigma-\mu}\in K^p$ and $\mu\in{\bf F}_p$. We compute explicitly
the decomposition of the prime $p$ in the subfields $M$ of $S$ of degree
$[M:\Q]=p$.

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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys