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Recognition of finite exceptional groups of Lie type


Authors: Martin W. Liebeck and E. A. O’Brien
Journal: Trans. Amer. Math. Soc. 368 (2016), 6189-6226
MSC (2010): Primary 20C20, 20C40
Published electronically: December 2, 2015
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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 $ \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 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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Additional Information

Martin W. Liebeck
Affiliation: Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom
Email: m.liebeck@imperial.ac.uk

E. A. O’Brien
Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
Email: e.obrien@auckland.ac.nz

DOI: https://doi.org/10.1090/tran/6534
Received by editor(s): October 10, 2013
Received by editor(s) in revised form: August 7, 2014
Published electronically: December 2, 2015
Article copyright: © Copyright 2015 American Mathematical Society