The primary decomposition of the factor group K (G)‎

الملخص EN

The main purpose of this work is to find the primary decomposition of the factor group K (G) = cf (G, Z) / (G) (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, Z┬p〖(n),〗 p = 5.

This work depends on finding the rational valued character matrix = * (Z┬5(n))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 work.