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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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/

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