The problem of finding the cyclic decomposition (c.d.) for the groups ), where prime upper than 9 is determined in this work. Also, we compute the Artin characters (A.ch.) and Artin indicator (A.ind.) for the same groups, we obtain that after computing the conjugacy classes, cyclic subgroups, the ordinary character table (o.ch.ta.) and the rational valued character table for each group.
Reaction of  p-fluoro benzoic acid with the thiosemicarbazide and salcialdehyde gave the new bidentate ligand .The prepared ligand Identified by FT-I.R and U.V-Visible spectcopic technique .Treatment of the prepared   ligand   with following metal ions  M=Tb(III),Eu(III),Nd(III) and La(III) ,in ethanol with a (1:1) M:L ratio and at pH=7 yielded series of neutral complexes as the general formula  [M LCl (H O ]. The prepared complexes were characterized using (FT-IR, UV-Vis) spectra , melting point, molar conductivity measurements . chloride ion content were also evolution by (mhor method) . The proposed structure of the complexes using program , chem office 3D(2004) .
The δ-mixing of γ-transitions in 70As populated in the 32 70 70 33 Ge p n As (, ) γ reaction is calculated in the present work by using the a2-ratio methods. In one work we applied this method for two cases, the first one is for pure transition and the sacend one is for non pure transition, We take into account the experimental a2-coefficient for previous works and δ -values for one transition only.The results obtained are, in general, in a good agreement within associated errors, with those reported previously , the discrepancies that occur are due to inaccuracies existing in the experimental data of the previous works.
For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.
A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.
The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.