On Simplicity of the Projective Special Linear Groups

Abstract: In this thesis, we will be proving that the Projective special linear group PSL(m,K) is a simple group for all dimensions m and finite fields K, with a few exceptions. First, we prove simplicity of PSL(2,K) (Jordan-Moore), and then move on to proving simplicity of PSL(m,K) (Jordan-Dickson) for all dimensions m >= 3. The most important tool used to prove this is by using certain linear transformations known as (elementary) transvections.