The Primary Decomposition of the Factor Group K(G)

Abstract

The main purpose of this work is to find the primary decomposition of the factorgroup K (The factor group of all Z-valued classfunctions module the group of Z-valued generalized characters for elementary Abeliangroup G), where G is a finite Abelian group of type , p=5.This work depends on finding the rational valued character matrixfrom the character table of and finding the invariant factors of this matrix, also wefound the general solution of this decomposition and prove it by mathematicalinduction. We have used the MATLAB program to calculate some results of thiswork.