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Unit Groups Of Central Simple Algebras And Their Frattini Subgroups

Barzegar, Farhad | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48866 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Hezavehi, Mohammad
  7. Abstract:
  8. Given a finite dimensional F-central simple algebra A = Mn(D),the connection between the Ferattini subgroup (A) and (F) via Z(A′), the center of the derived group of A , is investigated. Setting G = F \(A), it is shown that (F)Z(A′ ) G (\pFp)Z(A′)where the intersection is taken over primes p not dividing the degree of A. Furthermore ,when F is a local or global field, the group G is completely determined. Using the above connection, (A) is also calculated for some particular division rings D
  9. Keywords:
  10. Maximal Subgroup ; Division Rings ; Central Simple Algebras ; Frattini Subgroup

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