The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable
- 48 Downloads
LetD be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure ofD x (the multiplicative group ofD) can be reduced to questions about finite quotients ofD x. In this paper we prove that when deg(D)=3, finite quotients ofD x are solvable. the proof uses Wedderburn’s Factorization Theorem.
KeywordsNormal Subgroup Algebraic Group Division Algebra Multiplicative Group Finite Simple Group
Unable to display preview. Download preview PDF.
- M. Aschbacher,Finite Group Theory, Cambridge University Press, 1986.Google Scholar
- Y. Segev,On finite homomorphic images of the multiplicative group of a division algebra, Annals of Mathematics, to appear.Google Scholar
- Y. Segev and G. M. Seitz,Anisotropic groups of type A n and the commuting graph of finite simple groups, submitted.Google Scholar