Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosets of Sylow p-subgroups and a Question of Richard Taylor   We prove that for any prime p there exist infinitely many finite simple
groups G with a coset xP of a Sylow p-subgroup P of G such that every element
of xP has order divisible by p. John Thompson proved this for p=2 in 1967
answering a question of Lowell Paige. This result is used to answer a question
of Richard Taylor on adequate representations.

20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph