On the Classification of Extremely Primitive Affine Groups

Let G be a finite non-regular primitive permutation group on set Ω with point stabiliser Gα. Then is said to extremely if Gα acts primitively each of its orbits in \ {α}, which notion dating back work Manning the 1920s. By theorem Mann, Praeger and Seress, it known that every either almost simple or affine, all examples have subsequently been determined. Similarly, Mann et al. classified affine groups up finite, but undetermined, collection groups. Moreover, one assumes Wall’s conjecture number maximal subgroups an group, then there explicit list candidates, has eliminated recent paper by Burness Thomas. So, modulo conjecture, classification complete. In this we adopt different approach, allows us complete full generality, independent veracity otherwise setting. Our method relies Fawcett, Lee others existence regular acting irreducible modules.