The Burnside ring modulo a prime (Q1071107)

The author obtains extensive results on \(B_ p(G)=B(G)/pB(G)\), where \(B(G)\) is the Burnside ring of the finite group \(G\). These include calculation of the radical, the primitive idempotents, and the dimensions of the local direct factors. Applications are given to modular character theory, including a form of the Artin induction theorem. The example of the alternating group of degree five is treated in detail.