Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sylow-conjugate number fields   By a classical result of Neukirch and Uchida, a number field K is determined
by the structure of its absolute Galois group Gal(K). We show that K is not
determined by the structure of the Sylow subgroups of Gal(K), answering a
question raised by Florian Pop.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph