P-DECOMPOSITION MATRIX OF DERIVED CHEVALLEY GROUP

Muhammad Saleem; Sara Ghareeb; Mukhtar Ahmad; Ibrahim K. Alsulamie; Muhammad Muawwaz; Ather Qayyum

doi:10.5269/bspm.76757

Muhammad Saleem Department of Mathematics, NCBA&E Lahore, Multan sub-campus, Pakistan
Sara Ghareeb College of Basic Education, Kuwait
Mukhtar Ahmad Department of Mathematics, Khawja Fareed University of Engineering and Information Technology Rahim Yar Khan, Pakistan
Ibrahim K. Alsulamie Department of Science, King Abdulaziz Military Academy (KAMA), Riyadh 13959, Saudi Arabia
Muhammad Muawwaz Department of Mathematics, University of Southern Punjab Multan, Pakistan.
Ather Qayyum Institute of Mathematical Sciences, Universti Malaya, Malaysia

Abstract

Character theory has lot of applications in applied sciences specially it play a crucial role in computational chemistry, coding theory and quantum mechanics. In this research, p- decomposition matrices of the derived Chevalley group '(2) relative to all prime divisors of the group order have been computed. Our obtained results will be helpful to find the same results for the larger groups. Our research work is in continuous to our investigation of the decomposition matrices of finite groups. Here, we compute the absolutely irreducible p- characters of the Derived Chevalley group '(2) which is isomorphic to the group of all 33 matrices preserving a non- singular hermitian from over the field F9, relative to the all prime characteristic dividing the group order. The results are designed in decomposition matrices. Our work can be done by computer programming but we have done this by purely characters – theoretic.

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