Odd Characterisations of Finite Simple Groups |
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2-group 3-elements acts fixed point automorphism centralisation system character table character theory characterisation characters of G class function conjugacy class conjugate classes conjugate in G contains an element cyclic of order dihedral group dihedral of order divides G element of order elementary abelian group elementary abelian subgroup equation finite group finite number finite simple group fixed point free follows fragment of character G are conjugate G contains G is isomorphic G of order group G group of order integers involutions in G isomorphic to PSL Lemma M₁ M₂ maximal element minimal counterexample nilpotent normalised occurs odd order order 16 order 3 act permutation proof of Theorem Q₂ selfcentralisation simple C00-group simplicity of G special classes Stewart's Theorem subgroup of G subgroup of index subgroup of order Suzuki Suzuki group Sylow 2-subgroup system of type Taking H Theorem 9.2 weakly closed x+y+z+1