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

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- by Michael E. O’Nan PDF
- Trans. Amer. Math. Soc.
**214**(1975), 43-74 Request permission

## 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.## References

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## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**214**(1975), 43-74 - MSC: Primary 20B20
- DOI: https://doi.org/10.1090/S0002-9947-75-99942-0