Recognition of finite exceptional groups of Lie type

Abstract

Let $q$ be a prime power and let $G$ be an absolutely irreducible subgroup of $G{L}_d(F)$, 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 $G\ncong {}^3{D}_4(q)$ with $q$ even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle.

References in corpus (2)

• Recognising the Suzuki groups in their natural representations
• Recognising the small Ree groups in their natural representations