ON THE REDUCED NORM 1 GROUP OF A DIVISION ALGEBRA OVER A GLOBAL FIELD

Abstract

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