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., PSL(n, q), PSU(n, q), PSp(2n, q), P Ω^ϵ(n, q)), twisted Chevalley groups, and the Tits group.
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