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- Title
UNIT GROUPS OF CENTRAL SIMPLE ALGEBRAS AND THEIR FRATTINI SUBGROUPS.
- Authors
FALLAH-MOGHADDAM, R.; MAHDAVI-HEZAVEHI, M.; Rowen, L. H.
- Abstract
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 $ \Phi(F^*)Z(A') \subseteq G \subseteq (\bigcap_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.
- Subjects
GROUP theory; ALGEBRA; FRATTINI subgroups; DIMENSIONAL analysis; FINITE groups; DIVISION; RING theory
- Publication
Journal of Algebra & Its Applications, 2010, Vol 9, Issue 6, p921
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498810004300