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 Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 4, Pages 917–928 (Mi izv994)

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.

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

Bibliographic databases:

UDC: 512.7
MSC: Primary 20G30; Secondary 16K20

Citation: G. M. Tomanov, “On the group of reduced norm 1 group of a division algebra over a global field”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 917–928; Math. USSR-Izv., 39:1 (1992), 895–904

Citation in format AMSBIB
\Bibitem{Tom91}
\by G.~M.~Tomanov
\paper On~the~group of reduced norm~1 group of a division algebra over a global field
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 4
\pages 917--928
\mathnet{http://mi.mathnet.ru/izv994}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1137592}
\zmath{https://zbmath.org/?q=an:0789.20047}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 1
\pages 895--904
\crossref{https://doi.org/10.1070/IM1992v039n01ABEH002231}