A primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its orbits. We prove that finite extremely primitive groups are of affine type or almost simple. Moreover, we determine the affine type examples up to finitely many exceptions.
Cite this article
Avinoam Mann, Cheryl E. Praeger, Ákos Seress, Extremely primitive groups. Groups Geom. Dyn. 1 (2007), no. 4, pp. 623–660DOI 10.4171/GGD/27