In this paper we make a
contribution to the Margulis-Platonov conjecture, which describes the normal
subgroup structure of algebraic groups over number fields. We establish
the conjecture for inner forms of anisotropic groups of type An. We obtain
information on the commuting graph of nonabelian finite simple groups,
and consequently, using the paper by Segev, 1999, we obtain results on the
normal structure and quotient groups of the multiplicative group of a division
algebra.