Abstract
Let G be a finite group. The isomorphism classes of G-sets generate a commutative ring ℬ[ G] which we call the Burnside ring of G. We prove that ℬ[ G]⊗ Q is a semisimple algebra over Q and that formulas for certain primitive idempotents of this algebra yield the theorem of Artin on rational characters in a explicit form due to Brauer. The proof uses an isomorphism between ℬ[ G]⊗ Q and an algebra defined by the Möbius function of the partially ordered set of conjugacy classes of subgroups of G.
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