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Constructing Maximal Subgroups of Classical Groups

Published online by Cambridge University Press:  01 February 2010

Derek F. Holt  and
Colva M. Roney-Dougal
Derek F. Holt
Affiliation:
Mathematics Institute, The University of Warwick, Coventry, CV4 7AL, United Kingdom, [email protected], http://www.maths.warwick.ac.uk/~dfh/
Colva M. Roney-Dougal
Affiliation:
School of Computer Science, The University of St. Andrews, Fife KY16 9SS, United Kingdom, [email protected], http://www.dcs.st-and.ac.uk/~colva/

Abstract

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The maximal subgroups of the finite classical groups are divided by a theorem of Aschbacher into nine classes. In this paper, the authors show how to construct those maximal subgroups of the finite classical groups of linear, symplectic or unitary type that lie in the first eight of these classes. The ninth class consists roughly of absolutely irreducible groups that are almost simple modulo scalars, other than classical groups over the same field in their natural representation. All of these constructions can be carried out in low-degree polynomial time.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 46 - 79
Copyright
Copyright © London Mathematical Society 2005

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