On the group of reduced norm 1 group of a division algebra over a global field

It is proved that if the Platonov–Margulis conjecture on the standard structure of normal subgroups holds for the division algebras of index , then it also holds for the division algebras of index $n=2^mr$, for any $m$. Thus the conjecture is proved for the division algebras of index $2^m$, for any $m$, and its proof in the general case is reduced to the case of division algebras of odd index.