Modular Conjectures for Direct Product of Finite Groups

Abstract

I would like to thank Allah Almighty for my success in satisfactorily presenting this thesis and facilitating me in its planning and writing. I am glad to thank my supervisor Professor: Ahmad Alghamdi for suggesting the problem, which is the basis of this thesis, and for his useful knowledge, outstanding giving, and continuous guidance. Without his patient guidance and ingenious insights, it would be impossible for me to nish this thesis. It is my great fortune I work under his supervision in completing this thesis, and whatever phrases and sentences I write, the words of thanks remain unable to ful ll his rights. So, may God reward him with all good and make that in the balance of his good deeds. Special thanks to my university Umm Al-Qura University for giving me this golden oppor- tunity to realize my dream. I am ever grateful to my parents, who instilled a love for knowledge from a young age. They o ered me all dear and precious, and they have the merit after God for what I reach. I can only pray for them for long life, good work, and the attainment of paradise. I wish to thank my brothers and sisters for their support and encouragement throughout my study.