A subset F of a finite transitive group G≤Sym(Ω) is intersecting if for any g,h∈F
there exists ω∈Ω such that ωg=ωh. The
\emph{intersection density} ρ(G) of G is the maximum of \left\{
\frac{|\mathcal{F}|}{|G_\omega|} \mid \mathcal{F}\subset G \mbox{ is
intersecting} \right\}, where Gω is the stabilizer of ω in G.
In this paper, it is proved that if G is an imprimitive group of degree pq,
where p and q are distinct odd primes, with at least two systems of
imprimitivity then ρ(G)=1. Moreover, if G is primitive of degree pq,
where p and q are distinct odd primes, then it is proved that ρ(G)=1, whenever the socle of G admits an imprimitive subgroup.Comment: 22 pages, a new section was added. Accepted in Journal of
Combinatorial Theory, Series