Geodesic
On the Primitivity of the Group Algebra
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 536-540

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

Let G be a group and F a field of arbitrary characteristic. In [4] Kaplansky asks under what conditions is F[G] primitive, where F[G] is the group algebra of G over F. We give some necessary conditions on G that F[G] be primitive and propose a conjecture. Definition. A ring R is primitive if it has a faithful irreducible right module.The above should really be considered as a definition of right primitive. One can analogously define left primitive and the two properties are not equivalent. For our purposes, the two concepts are equivalent, for the group algebra possesses a nice involution.If we assume that F[G] is primitive, there are some immediate restrictions on G. First of all G cannot be Abelian since the only primitive commutative rings are fields. (I exclude of course the case when G consists of one element.) 
Rosenberg, Alan. On the Primitivity of the Group Algebra. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 536-540. doi: 10.4153/CJM-1971-057-8
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