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ALMOST SIMPLE KGROUPS
The Finite Groups of Lie Type
Local Subgroups of Groups of Lie Type I
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2-subgroup according action acts adjoint algebraic group asserted assume Aut(K automorphism centralizes choose classes clearly closed column commutator completes the proof component conclude conjugate connected consequence consider contains contradiction corresponding covering cyclic defined definition determined dimension direct divides element elementary abelian endomorphism example exists fact factors field Finally finite fixed follows fundamental Furthermore given gives graph automorphism hand Hence holds implies induces Inndiag(K inner inverts involutions irreducible isomorphism Lemma Lie(r lies listed mapping maximal torus module Moreover nontrivial normalizes notation Note parabolic subgroup particular permutes positive possibilities preimage prime proof properties Proposition prove remains remark representation respectively result root root system satisfy simple space Steinberg structure Suppose Sylow Table Theorem trivial unique universal weight whence write yields