LMS Journal of Computation and Mathematics

Research Article

Constructing Maximal Subgroups of Classical Groups

Derek F. Holta1 and Colva M. Roney-Dougala2

a1 Mathematics Institute, The University of Warwick, Coventry, CV4 7AL, United Kingdom, dfh@maths.warwick.ac.uk, http://www.maths.warwick.ac.uk/~dfh/

a2 School of Computer Science, The University of St. Andrews, Fife KY16 9SS, United Kingdom, colva@dcs.st-and.ac.uk, http://www.dcs.st-and.ac.uk/~colva/

Abstract

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.

(Received March 04 2004)

(Revised November 02 2004)

(Accepted February 15 2005)