Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kummerian Property and Maximal Pro-$p$ Galois Groups   For a prime number $p$, we give a new restriction on pro-$p$ groups $G$ which
are realizable as the maximal pro-$p$ Galois group $G_F(p)$ for a field $F$
containing a root of unity of order $p$. This restriction arises from Kummer
Theory and the structure of the maximal $p$-radical extension of $F$. We study
it in the abstract context of pro-$p$ groups $G$ with a continuous homomorphism
$\theta\colon G\to1+p\mathbb{Z}_p$, and characterize it cohomologically, and in
terms of 1-cocycles on $G$. This is used to produce new examples of pro-$p$
groups which do not occur as maximal pro-$p$ Galois groups of fields as above.

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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an