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

O’Nan, Michael E.

doi:10.1090/S0002-9947-75-99942-0

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

Trans. Amer. Math. Soc. 214 (1975), 43-74

DOI: https://doi.org/10.1090/S0002-9947-75-99942-0

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Abstract:

The main result is that the socle of the point stabilizer of a doubly-transitive permutation group is abelian or the direct product of an abelian group and a simple group. Under certain circumstances, it is proved that the lengths of the orbits of a normal subgroup of the one point stabilizer bound the degree of the group. As a corollary, a fixed nonabelian simple group occurs as a factor of the socle of the one point stabilizer of at most finitely many doubly-transitive groups.

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