Seuri Basilio Kuosmanen: Classical finite simple groups

Abstract

This paper aims to prove the simplicity of the projective special linear groups and the projective symplectic groups, which both belong to the family of six classical simple finite groups. To do this, we first give intuition and motivation for studying simple groups and give some prerequisite knowledge about group theory. We then proceed to prove Jordan-Hölder Theorem, by applying, Schreier's Refinements Theorem. For the main result of this thesis, we use Iwasawa's Lemma.