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