Loading...

A Criterion for the Triviality of G(D) and Its Applications to the Multiplicative Structure of D

Shahosseini، Ehsan | 2014

503 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47906 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Hezavehi, Mohammad
  7. Abstract:
  8. Let D be an F-central division algebra of index n. Here we present a criterion for the triviality of the group G(D) = D*=NrdD=F (D*)D′ and thus generalizing various related results published recently. To be more precise, it is shown that G(D) = 1 if and only if SK1(D) = 1 and F*2 = F*2n . Using this, we investigate the role of some particular subgroups of D* in the algebraic structure of D. In this direction, it is proved that a division algebra D of prime index is a symbol algebra if and only if D* contains a non-abelian nilpotent subgroup. More applications of this criterion including the computation of G(D) and the structure of maximal subgroups of D* are also investigated
  9. Keywords:
  10. Division Rings ; Henslian Valuation ; Nonabelian Divisible Group ; Central Simple Algebras

 Digital Object List