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 . 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 ...

Start Free Trial

No credit card required