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Recognition of finite exceptional groups of Lie type

Recognition of finite exceptional groups of Lie type

Let $q$ be a prime power and let $G$ be an absolutely irreducible subgroup of $GL_d(F)$, where $F$ is a finite field of the same characteristic as $\mathbb {F}_q$, the field of $q$ elements. Assume that $G \cong G(q)$, a quasisimple group of exceptional Lie type over $\mathbb {F}_q$ which …