Loading...

Unit groups of central simple algebras and their Frattini subgroups

Fallah Moghaddam, R ; Sharif University of Technology | 2010

133 Viewed
  1. Type of Document: Article
  2. DOI: 10.1142/S0219498810004300
  3. Publisher: 2010
  4. Abstract:
  5. Given a finite dimensional F-central simple algebra A = Mn(D), the connection between the Frattini subgroup Φ(A*) and Φ(F*) via Z(A′), the center of the derived group of A*, is investigated. Setting G = F* ∩ Φ(A*), it is shown that Φ (F*)Z(A′) ⊂ G ⊂ (∩p F*p) 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, Φ(A*) is also calculated for some particular division rings D
  6. Keywords:
  7. Division ring ; Frattini subgroup ; Maximal subgroup
  8. Source: Journal of Algebra and its Applications ; Volume 9, Issue 6 , December , 2010 , Pages 921-932 ; 02194988 (ISSN)
  9. URL: http://www.worldscientific.com/doi/abs/10.1142/S0219498810004300