Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intersection density of transitive groups of certain degrees   Two elements $g$ and $h$ of a permutation group $G$ acting on a set $V$ are
said to be intersecting if $g(v) = h(v)$ for some $v \in V$. More generally, a
subset ${\cal F}$ of $G$ is an intersecting set if every pair of elements of
${\cal F}$ is intersecting. The intersection density $\rho(G)$ of a transitive
permutation group $G$ is the maximum value of the quotient $|{\cal F}|/|G_v|$
where ${\cal F}$ runs over all intersecting sets in $G$ and $G_v$ is a
stabilizer of $v\in V$. In this paper the intersection density of transitive
groups of degree twice a prime is determined, and proved to be either $1$ or
$2$. In addition, it is proved that the intersection density of transitive
groups of prime power degree is $1$.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn