Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbits of Sylow subgroups of finite permutation groups   We say that a finite group $G$ acting on a set $\Omega$ has Property $(*)_p$
for a prime $p$ if $P_\omega$ is a Sylow $p$-subgroup of $G_\omega$ for all
$\omega\in\Omega$ and Sylow $p$-subgroups $P$ of $G$. Property $(*)_p$ arose in
the recent work of Tornier (2018) on local Sylow $p$-subgroups of Burger-Mozes
groups, and he determined the values of $p$ for which the alternating group
$A_n$ and symmetric group $S_n$ acting on $n$ points has Property $(*)_p$. In
this paper, we extend this result to finite $2$-transitive groups and we give a
structural characterisation result for the finite primitive groups that satisfy
Property $(*)_p$ for an allowable prime $p$.

14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph