The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable

Abstract

LetD be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure ofDx (the multiplicative group ofD) can be reduced to questions about finite quotients ofDx. In this paper we prove that when deg(D)=3, finite quotients ofDx are solvable. the proof uses Wedderburn’s Factorization Theorem.