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2-subgroups 2-Sylow alternating group Amer author proves automorphisms Berkovic Brauer Bull Burnside character theory characters Chevalley groups classical groups collineation group commutator group composite order conjugate Coxeter cubic surface cyclic defined Dickson Dieudonne doubly transitive finite group finite simple groups Frobenius G is isomorphic Galois field geometrically Gives group G group of degree group of odd group of order Gruppen icosahedral group invariant involutions irreducible representations Let G Lie algebra linear fractional group linear groups linear homogeneous London Math Math Reviews Mathieu groups matrices maximal subgroups Miller nilpotent normal subgroup odd order odd prime order 60 order g orthogonal group paper partition permutation group polytopes prime number Proc proof PSL(n,q Shows solvable Steinberg subgroup of G subgroup of index subgroup of order substitutions Suzuki Sylow subgroups symplectic group Szep theory Tits Todd Trans transitive groups transitive permutation group Uber