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Journal of the London Mathematical Society 2005 71(2):345-361; doi:10.1112/S0024610704006179
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© The London Mathematical Society

Maximal Subgroups of Large Rank in Exceptional Groups of Lie Type

Martin W. Liebeck and Gary M. Seitz

Department of Mathematics, Imperial College London SW7 2BZ, United Kingdom
Department of Mathematics, University of Oregon Eugene, OR 97403, USA

Received 16 February 2004. Revision received 7 July 2004.

Let G = G(q) be a finite almost simple exceptional group of Lie type over the field of q elements, where q = pa and p is prime. The main result of the paper determines all maximal subgroups M of G(q) such that M is an almost simple group which is also of Lie type in characteristic p, under the condition that rank(M) > 1/2 rank(G). The conclusion is that either M is a subgroup of maximal rank, or it is of the same type as G over a subfield of Fq, or (G, M) is one of (Formula, F4(q)), (Formula, C4(q)), (E7(q), 3D4(q)). This completes work of the first author with Saxl and Testerman, in which the same conclusion was obtained under some extra assumptions.


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