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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 5, Pages 983–994 (Mi izv1998)  

The radical of the group algebra of a solvable group is locally nilpotent

A. E. Zalesskii


Abstract: A formula is given which expresses the Jacobson radical of the group algebra of a solvable group in terms of the radical of a certain simply constituted normal subgroup. In particular, for a finitely generated group the radical is the union of nilpotent ideals and is generated by the radicals of the group rings of finite normal subgroups.

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:5, 979–990

Bibliographic databases:

UDC: 519.4
MSC: Primary 16A21, 16A26, 20E15; Secondary 20E25, 20F50
Received: 11.12.1972

Citation: A. E. Zalesskii, “The radical of the group algebra of a solvable group is locally nilpotent”, Izv. Akad. Nauk SSSR Ser. Mat., 38:5 (1974), 983–994; Math. USSR-Izv., 8:5 (1974), 979–990

Citation in format AMSBIB
\Bibitem{Zal74}
\by A.~E.~Zalesskii
\paper The radical of the group algebra of a~solvable group is locally nilpotent
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 5
\pages 983--994
\mathnet{http://mi.mathnet.ru/izv1998}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=357568}
\zmath{https://zbmath.org/?q=an:0297.16008}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 5
\pages 979--990
\crossref{https://doi.org/10.1070/IM1974v008n05ABEH002135}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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