The Solvablitiy Degree of the Alternation Group

Let G be a finite group. ##The sylowility degree is given by PrSy(G) = |{(x,y)∈G×G|⟨x,y⟩≤SyG,∀x,y∈G}| |G|2 and the sylow graph ΓG(V, E) = ΓSy is defined by the set of all vertices of E(ΓSy) = {{x, y} | ⟨x, y⟩ ≤Sy G}. ##In this seminar, we establish some properties of the sylow graph defined by group D2n and study the relation between ΓSy and PrSy(G).