Let p, e be distinct primes and let q be a power of p. We denote by Fq the finite field with q-elements. Let G be a connected compact Lie group. There exists a reductive finite algebraic group G(C) associated with G, called the complexification of G. One may consider G(C) as C-rational points of the reductive integral algebraic group scheme G_Z. Taking the Fq-rational points of Gz, we have the finite Chevalley group G(Fq).
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