This article is cited in 1 paper

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

G. M. Tomanov

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Abstract: 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.

UDC: 512.7

MSC: Primary 20G30; Secondary 16K20

Received: 11.03.1991

 English version: Mathematics of the USSR-Izvestiya, 1992, 39:1, 895–904

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