Ollie Clarke

A Recipe for Finite Groups of Lie Type

Simple groups of Lie type are listed as one of the three infinite families of finite simple groups. The other infinite families are very familiar namely the cyclic groups of prime order and the alternating groups A_n for n >= 5. So what are these groups of Lie type?

We will construct these groups starting from scratch using results from Lie algebras and group theory. Once constructed we will look at the Chevalley groups and get a better feel for them by seeing many of their important subgroups. We will also glimpse my masters project in which focuses on the parabolic subgroups of A2(q), B2(q) and G2(q).