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On the subgroup structure of exceptional groups of Lie type

Author(s): Martin W. Liebeck; Gary M. Seitz
Journal: Trans. Amer. Math. Soc. 350 (1998), 3409-3482.
MSC (1991): Primary 20G40, 20E28
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Abstract: We study finite subgroups of exceptional groups of Lie type, in particular maximal subgroups. Reduction theorems allow us to concentrate on almost simple subgroups, the main case being those with socle $X(q)$ of Lie type in the natural characteristic. Our approach is to show that for sufficiently large $q$ (usually $q>9$ suffices), $X(q)$ is contained in a subgroup of positive dimension in the corresponding exceptional algebraic group, stabilizing the same subspaces of the Lie algebra. Applications are given to the study of maximal subgroups of finite exceptional groups. For example, we show that all maximal subgroups of sufficiently large order arise as fixed point groups of maximal closed subgroups of positive dimension.

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Additional Information:

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

Gary M. Seitz
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: seitz@math.uoregon.edu

DOI: 10.1090/S0002-9947-98-02121-7
PII: S 0002-9947(98)02121-7
Received by editor(s): October 11, 1996
Additional Notes: The authors acknowledge the support of NATO Collaborative Research Grant CRG 931394. The second author also acknowledges the support of an NSF Grant
Copyright of article: Copyright 1998, American Mathematical Society

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