Geodesic
Group Algebras With Central Radicals
Glasgow mathematical journal, Tome 5 (1962) no. 3, pp. 103-108

Voir la notice de l'article provenant de la source Cambridge University Press

It is well known that when the characteristic p(≠ 0) of a field divides the order of a finite group, the group algebra possesses a non-trivial radical and that, if p does not divide the order of the group, the group algebra is semi-simple. A group algebra has a centre, a basis for which consists of the class-sums. The radical may be contained in this centre; we obtain necessary and sufficient conditions for this to happen. 
Wallace, D. A. R. Group Algebras With Central Radicals. Glasgow mathematical journal, Tome 5 (1962) no. 3, pp. 103-108. doi: 10.1017/S2040618500034419
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