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arXiv · 1310.2978

Recognition of finite exceptional groups of Lie type

Martin W. Liebeck·E. A. O'Brien
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Abstract

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 $\F_q$, the field of $q$ elements. Assume that $G \cong G(q)$, a quasisimple group of exceptional Lie type over $\F_q$ 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 $G \not\cong {}^3 D_4(q)$ with $q$ even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle.

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Martin W. Liebeck, E. A. O'Brien. 2014-09-02. Recognition of finite exceptional groups of Lie type. https://arxiv.org/abs/1310.2978

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