For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio

This research aims to study the important of the effect of analysis of covariance manner for one of important of design for multifactor experiments, which called split-blocks experiments design (SBED) to deal the problem of extended measurements for a covariate variable or independent variable (X) with data of response variable or dependent variable Y in agricultural experiments that contribute to mislead the result when analyze data of Y only. Although analysis of covariance with discussed in experiments with common deign, but it is not found information that it is discussed with split-Blocks experiments design (SBED) to get rid of the impact a covariance variable. As part application actual field experiment conducted, begun at

In this research we present An idea of setting up same split plots experiments in many locations and many periods by Latin Square Design. This cases represents a modest contribution in area of design and analysis of experiments. we had written (theoretically)  the general plans, the mathematical models for these experiments, and finding the derivations of EMS for each component (source) of sources of variation of the analysis of variance tables which uses for the statistical analysis for these expirements