Abstract
Let q be a prime power and let G be an absolutely irreducible subgroup of GLd(F ), where F is a finite field of the same characteristic as Fq, the field of q elements. Assume that G ∼= G(q), a quasisimple group of exceptional Lie type over Fq which is neither a Suzuki nor a Ree group. We present a Las Vegas algorithm that constructs an isomorphism from G to the standard copy of G(q). If G 6∼= 3D4(q) with q even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle.
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