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The Maximal Subgroups of the Low-Dimensional Finite Classical Groups by Colva M. Roney-Dougal, Derek F. Holt, John N. Bray

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3Geometric maximal subgroups

The maximal subgroups of the finite classical groups are divided into two broad classes by Aschbacher’s theorem (see Theorem 2.1.5 for a rough statement): the geometric subgroups and those in Class image. In this chapter we shall classify those subgroups that are maximal amongst the geometric subgroups of the finite classical groups in dimension up to 12.

For a more precise statement, first recall Definition 2.1.2 of the geometric subgroups, our dimension assumptions from Definition 1.6.20, and the more precise version of Aschbacher’s theorem given in Theorem 2.2.19. Let G be an almost simple with socle S, where S is simple ...

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