Geodesic
Remarks on the commutativity of the radicals of group algebras
Glasgow mathematical journal, Tome 20 (1979) no. 1, pp. 63-68

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Let K be an arbitrary field with characteristic p > 0, G a finite group of order pag′ with (p, g′) = 1, P a p-Sylow subgroup of G and G′ the commutator subgroup of G. For a ring R denote by J(R) the Jacobson radical of R and by Z(R) the centre of R. We write KG for the group algebra of G over K. 
Koshitani, Shigeo. Remarks on the commutativity of the radicals of group algebras. Glasgow mathematical journal, Tome 20 (1979) no. 1, pp. 63-68. doi: 10.1017/S0017089500003736
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