Geodesic
On the Semisimplicity of Modular Group Algebras. II
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1137-1145

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

Let G be a discrete group, let Kbe an algebraically closed field of characteristic p > 0 and let KGdenote the group algebra of Gover K.In a previous paper (2) I studied the Jacobson radical JKGof KGfor groups Gwith big abelian subgroups or quotient groups. It is therefore natural to next consider metabelian groups, and I do this here. The main result is as follows.THEOREM 1. Let K be an algebraically closed field of characteristic p and let a group G have a normal abelian subgroup A with G/A abelian. Then JKG ≠ {0} if and only if G has an element g of order p such that the A-conjugacy class gA is finite and such that the group is periodic.Note that since and G/Ais abelian, we do in fact have . 
Passman, D. S. On the Semisimplicity of Modular Group Algebras. II. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1137-1145. doi: 10.4153/CJM-1969-124-8
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[1] 1. Passman, D. S., Nil ideals in group rings, Michigan Math. J. 9 (1962), 375–384. Google Scholar

[2] 2. Passman, D. S., On the semisimplicity of modular group algebras, Proc. Amer. Math. Soc. 20 (1969), 515–519. Google Scholar

[3] 3. Scott, W. R., Group theory (Prentice-Hall, Englewood Cliffs, N.J., 1964). Google Scholar

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