Some primitive actions in G2(q)

This thesis investigates a class of simple groups and provides detailed knowledge about some of their primitive actions on cosets of maximal-rank subgroups. Groups are mathematical objects capturing the concept of symmetry. Finite simple groups form the building blocks of finite groups. This research utilises specialised techniques and the theory of both finite groups and algebraic groups. The results provide a deeper mathematical understanding of the geometric and algebraic structure of groups of exceptional Lie type, which is significant for advancements in group theory and representation theory.