College of Education for Pure Science

In fulfillment of the fourth goal of the Sustainable Development Goals (Quality Education), a master’s thesis entitled “Calculating Hopf-Gallo Structures in Irregular Extensions of the Metacyclic Group of Order pqr” was defended in the College of Education for Pure Science at the University of Mosul on Thursday, July 31, 2025.
Part of the thesis defense was attended by the Dean of the College, Professor Dr. Jassim Fatehi Ali, the Assistant Dean for Academic Affairs, Assistant Professor Dr. Azzam Salahuddin Younis, and a number of faculty members from the department.
The study, presented by the student Shahad Khalil Douri Khalil Al-Douri from the Department of Mathematics, addressed all Hopf-Gallo structures on the irregular L/K expansions of the metacyclic group of order pqr. The transitive subgroups of Hol(G) of order pqr^2, 2pqr^2, pqr, 2pqr were identified, and the transitive subgroups of Hol(G) of order divisible by p^2 q^2 r were identified. The Hopf-Gallo structures on the transitive subgroups of Hol(G) were also enumerated and calculated in detail for the following orders: pqr, 2pqr, pqr^2, 2pqr^2, p^2 q^2 r 2p^2 q^2 r, p^2 q^2 r^2, 2p^2 q^2 r^2.
The discussion committee was chaired by Professor Dr. Nada Yaseen Qasim, and Professor Dr. Mahdi Saleh Nayef and Lecturer Dr. Luma Ahmed Khalil as members, and Assistant Professor Dr. Ali Abdul-Qader Bilal as both member and supervisor. The Dean of the College presented a letter of thanks and appreciation to Professor Dr. Mahdi Saleh Nayef from the College of Education at Al-Mustansiriya University for his efforts in traveling and participating in the student’s discussion.
The master’s thesis was accepted. Congratulations to the student and her supervisor on this scientific achievement.

Division of Media and Government Communication
College of Education for Pure Science
Thursday, July 31, 2025