Geodesic
The radical of the group algebra of a~solvable group is locally nilpotent
Izvestiya. Mathematics , Tome 8 (1974) no. 5, pp. 979-990

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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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     author = {A. E. Zalesskii},
     title = {The radical of the group algebra of a~solvable group is locally nilpotent},
     journal = {Izvestiya. Mathematics },
     pages = {979--990},
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     volume = {8},
     number = {5},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_5_a1/}
}
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A. E. Zalesskii. The radical of the group algebra of a~solvable group is locally nilpotent. Izvestiya. Mathematics , Tome 8 (1974) no. 5, pp. 979-990. http://geodesic.mathdoc.fr/item/IM2_1974_8_5_a1/