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  "body": "\n## Summary\n\nA finite group of Lie type is the group of points of a reductive algebraic group that are fixed by a Frobenius-type map.\nAn example is $\\mathrm{GL}_n(\\F_q)$ inside $\\mathrm{GL}_n$ over the algebraic closure of $\\F_q$.\nThese groups are finite analogues of Lie groups, and their simple quotients form most of the families in the classification of finite simple groups.\nThey include the classical groups over finite fields, the Chevalley groups of exceptional type, and the twisted groups of Steinberg, Suzuki and Ree.\n\n## Explanations\n\n### L1 human\n\nMatrix groups such as invertible matrices or orthogonal matrices make sense over any field, including a finite field with $q$ elements.\nOver a finite field these groups are finite.\nFor example, $\\mathrm{SL}_2(\\F_2)$ is the group of $2 \\times 2$ matrices with entries in $\\{0, 1\\}$, arithmetic modulo $2$ and determinant $1$; it has $6$ elements and is isomorphic to $S_3$.\nGroups built this way, and their twisted relatives, are the groups of Lie type.\nTheir simple quotients, such as $\\mathrm{PSL}_n(\\F_q)$, are the main source of finite simple groups.\n",
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