Anisotropic groups of type A_n and the commuting graph of finite simple groups

In this paper we make a contribution to the Margullis-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 A_n. 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.