On estimate of the order of primitive permutation groups
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 256-263

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Let $G$ be a primitive permutation group of degree $n$. Then $|G|\le nd^m$, where $d$ is the minimal order of a nontrivial orbit of the stabilizer of $G$ and $m$ is the minimal degree of a nonunity irreducible representation of $g$ occuring the permutation representation. Bibliography: 8 titles.
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     title = {On estimate of the order of primitive permutation groups},
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I. N. Ponomarenko. On estimate of the order of primitive permutation groups. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 256-263. http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a16/