Linear Groups Containing a Singer Cycle*
نویسنده
چکیده
I f G induces a primitive permutation group on the set X of points (l-spaces) of the underlying vector space V, then well-known results of Burnside [I, p. 3411 and Schur [6] imply that G acts on X 2-transitively or as a regular or Frobenius group of prime degree; the theorem then follows from [2; 51. We must thus take a nontrivial block of imprimitivity d for G on X, and analyze the action of G on do. It should be noted that the proof is elementary in the same sense as in [2]: no purely group theoretic classification theorems are required.
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