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

G. M. Tomanov

Izvestiya. Mathematics , Tome 39 (1992) no. 1, pp. 895-904.

Résumé

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.

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