Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Demushkin groups and inverse Galois theory for pro-p-groups of finite
  rank and maximal p-extensions   This paper proves that if $E$ is a field, such that the Galois group
$\mathcal{G}(E(p)/E)$ of the maximal $p$-extension $E(p)/E$ is a Demushkin
group of finite rank $r(p)_{E} \ge 3$, for some prime number $p$, then
$\mathcal{G}(E(p)/E)$ does not possess nontrivial proper decomposition groups.
When $r(p)_{E} = 2$, it describes the decomposition groups of
$\mathcal{G}(E(p)/E)$. The paper shows that if $(K, v)$ is a $p$-Henselian
valued field with $r(p)_{K} \in \mathbb N$ and a residue field of
characteristic $p$, then $P \cong \widetilde P$ or $P$ is presentable as a
semidirect product $\mathbb Z_{p}^{\tau} \rtimes \widetilde P$, for some $\tau
\in \mathbb N$, where $\widetilde P$ is a Demushkin group of rank $\ge 3$ or a
free pro-$p$-group. It also proves that when $\widetilde P$ is of the former
type, it is continuously isomorphic to $\mathcal{G}(K ^{\prime}(p)/K
^{\prime})$, for some local field $K ^{\prime}$ containing a primitive $p$-th
root of unity.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga