  It was first shown by Cameron and Ku that the group $G=Sym(n)$ has the strict
EKR property. Then Godsil and Meagher presented an entirely different proof of
this fact using some algebraic properties of the symmetric group. A similar
method was employed to prove that the projective general linear group
$PGL(2,q)$, with its natural action on the projective line $\mathbb{P}_q$, has
the strict EKR property. The main objective in this thesis is to formally
introduce this method, which we call the module method, and show that this
provides a standard way to prove Erdos-Ko-Rado theorems for other permutation
groups. We then, along with proving Erdos-Ko-Rado theorems for various groups,
use this method to prove some permutation groups have the strict EKR property.
We will also show that this method can be useful in characterizing the maximum
independent sets of some Cayley graphs. To explain the module method, we need
some facts from representation theory of groups, in particular, the symmetric
group. We will provide the reader with a sufficient level of background from
representation theory as well as graph theory and linear algebraic facts about
graphs.
