Normal structure of the one-point stabilizer of a doubly-transitive permutation group. I

O’Nan, Michael E.

doi:10.1090/S0002-9947-1975-0393207-3

Normal structure of the one-point stabilizer of a doubly-transitive permutation group. I
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by Michael E. O’Nan PDF

Trans. Amer. Math. Soc. 214 (1975), 1-42 Request permission

Abstract:

Let G be a doubly-transitive permutation group on a finite set X and x a point of X. Let ${N^x}$ be a normal subgroup of ${G_x}$, the subgroup fixing x, such that ${N^x}$ is a T.I. set and not semiregular on $X - x$. Then, $PSL(n,q) \subseteq G \subseteq P\Gamma L(n,q)$. Geometrical consequences of this result are also obtained.

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