Group of Lie type

Summary

A finite group of Lie type is the group of points of a reductive algebraic group that are fixed by a Frobenius-type map. An example is $\mathrm{GL}_n(\F_q)$ inside $\mathrm{GL}_n$ over the algebraic closure of $\F_q$. These groups are finite analogues of Lie groups, and their simple quotients form most of the families in the classification of finite simple groups. They include the classical groups over finite fields, the Chevalley groups of exceptional type, and the twisted groups of Steinberg, Suzuki and Ree.