Simple Group Psl (3, P) Permutation On The Subgroup Of Pgl (2, P)

Suppose that G is a permutation group on the finite set Ω. Let G_α = {g ∈ G | α~9 = α} be the point stabilizer of G, for any a ∈ Ω. Then the orbits of G_α on Ω are called the suborbits of G relative to α, while {α} is said to be trivial. A nonempty subset A is called a block of G if △~x = △ or △~x ∩ △ = (?), (?)x ∈ G. Clearly every subset containing only one point and Ω itself is a block, called trivial blocks. The group G is said to be primitive if there exists no nontrivial block on Ω. It is well-known that G is primitive if and only if G_α is maximal in G for any α ∈ ΩIn this thesis, we consider the action of PSL(3,p) on the set of right cosets of a maximal subgroup PGL(2,p) by the right multiplication, and determine the suborbits of this primitive group, while it is assumed that p ≡ 61(mod 120), for a convenience.