Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable
Rapinchuk A, Segev Y, Seitz G. Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Journal of the Amer. Math. Soc. 2002;15(4):929–978.