On a theorem of Wielandt for finite primitive permutation groups

Let G be a finite primitive permutation group with a non-trivial, non-regular normal subgroup N, and let Gamma be an orbit of a point stabilizer N-alpha. Then each composition factor S of N-alpha occurs as a section of the permutation group induced by N-alpha on Gamma. 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.