Transitive Extensions of Certain Permutation Groups of Rank 3

Abstract

We denote a permutation group H on a set Γ by (H, Γ) . (H, Γ) is called a permutation group of rank 3 if (H, Γ) is transitive and (H a , Γ), a ∈ Γ , has exactly three orbits, where H a is the stabiliger of a point a , namely, {α ∈ H \a α = a}