On a theorem of Wielandt for finite primitive permutation groups

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Let G be a finite primitive permutation group with a non-trivial, non-regular normal subgroup N, and let γ be an orbit of a point stabilizer Nα. Then each composition factor S of N α occurs as a section of the permutation group induced by Nα on F. The case N = G is a theorem of Wielandt. The general result and some of its corollaries are useful for studying automorphism groups of combinatorial structures.