A Lie group is a group with the structure of a manifold. Therefore, discrete groups do not count. However, the most useful Lie groups are defined as subgroups of some matrix group. The analogous subgroups where the matrices are taken to be over a finite field (but the group is defined in the same way) are called the Lie-type groups. They are a kind of linear algebraic group. The Lie-type groups include the Chevalley groups (i.e., P S L(n, q), P S U(n, q), P S p(2n, q), P Ω^ϵ(n, q)), twisted Chevalley groups, and the Tits group.

Chevalley groups | finite group | Lie group | orthogonal group | simple group | symplectic group | Tits group | twisted Chevalley groups | unitary group

Marius Sophus Lie