Generation of certain groups by three involutions, two of which commute

In this thesis the question of generating PSLn( q) with three involutions, two of which commute is completely settled. When such a generation is possible we explicitly supply the generators as well as all computations that would enable one to write any particular matrix in terms of these generators.;We also provide a complete classification (up to conjugacy) of embeddings of the Klein 4-group into PSLn(q) over finite fields of odd characteristic and explicitly list representatives of each embedding.