عهود عايد هادي الجبوري

In this paper, we introduce a new parameter to compute the normality degree of dihedral group P_Nor (D_2n) and normal graph Γ_Nor (D_2n) of it is done, so we presented the relation between parameter normality degree and normal graph and we find the degrees of the vertices of the normal graph. We describe the structure of elements that realize the normality degree for the dihedral group. It is evident that the study begin here can successfully be expanded to other classes of finite groups. This will be of interest to us in future research.

In this paper we studied the cyclicity parameter of dihedral group D_2n and we introduced algorithm to compute these parameter.

Let G be a fnite group. The normality degree is given by Pnd(G) = |{(x,y)∈G×G|⟨|Gx,y |2⟩EG,∀x,y∈G}| and the normal graph ΓG(V, E) = ΓN is defned by the set of all vertices of E(ΓN) = {{x, y} | ⟨x, y⟩ E G}. In this paper, we establish some properties of the normal graph defned by group D2n and study the relation between ΓN and Pnd(G).

We will present a new parameter to compute the Sylow degree Sy(Cn) of cyclic group Cn.

We will present a new parameter to compute the Sylow degree P_Sy (C_n) of cyclic group〖 C〗_n ,and we will find the relationship between this parameter and the Sylow graph. Also we will apply the same tecnique with the dyhedral group D_2n.

This paper explores the decomposition of pre-