###### SOME ADVANCED RESULTS ON CO-HOMOLOGY GROUP OF K(Z,n)

**Hero Mawlood Salih**

Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah, Iraq.

** **

**Hardi Nasradin Aziz**

Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah, Iraq.

** **

**Hardi Ali Shareef**

Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah, Iraq.

E-mail: hero.salh@univsul.edu.iq1, harde.aziz@univsul.edu.iq and hardy.shareef@univsul.edu.iq

*Corresponding author: hardy.shareef@univsul.edu.iq

*ORCID ID: 0000-0003-2798-1921

**Abstract:**

The purpose of having the serre- spectral sequence is to compute co-homology, in particular when we have a fibration F → E → B. This study discusses Eilenberg macLane spaces and their co-homology groups. We use the method of spectral sequence to construct the cohomology of K(Z,n), and respectively we can express topological groups of (n − 1)- connected space X by K(Z,n). The main purpose of this paper is to compute co-homology groups of Eilenberg-MacLane space K(Z,6) and K(Z,7).

**Key words:** Homology group, Co-homology group, Spectral sequence, Serre spectral sequence.