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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Black box exceptional groups of Lie type


Authors: W. M. Kantor and K. Magaard
Journal: Trans. Amer. Math. Soc. 365 (2013), 4895-4931
MSC (2010): Primary 20D06, 20G40; Secondary 20B40, 20G41, 20P05, 68Q25
Published electronically: May 28, 2013
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Abstract: If a black box group is known to be isomorphic to an exceptional simple group of Lie type of (twisted) rank $ >1$, other than any $ ^2\kern -.8pt F_4(q)$, over a field of known size, a Las Vegas algorithm is given to produce a constructive isomorphism. In view of its timing, this algorithm yields an upgrade of all known nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to any group $ ^2\kern -.8pt F_4(q)$ or $ ^2G_2(q)$.


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Additional Information

W. M. Kantor
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: kantor@uoregon.edu

K. Magaard
Affiliation: School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT United Kingdom
Email: k.magaard@bham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05822-9
PII: S 0002-9947(2013)05822-9
Received by editor(s): November 1, 2009
Received by editor(s) in revised form: November 6, 2009, and December 13, 2011
Published electronically: May 28, 2013
Additional Notes: This research was supported in part by NSF grants DMS 9731421, DMS 0242983 and DMS 0753640, and NSA grant MDA-9049810020.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.